Still have math questions?

Ask our expert tutors
Recent Algebra Arithmetic Calculus Finance General Geometry Precalculus Probability Statistics Trigonometry Logic
Q:

Assume that \( 2 \) cards are drawn from a standard \( 52 \) -card deck. Find the following probabilities. 

a) Assume the cards are drawn without replacement. Find the probability of drawing a black card followed by a black card. 

b) Assume the cards are drawn with replacement. Find the probability of drawing a black card followed by a black card. 

a. The probability of drawing a black card followed by a black card without replacement is \( \frac { 25 } { 102 } \) . 

(Simplify your answer.)

b. The probability of drawing a black card followed by a black card with replacement is \( \square \) . 

(Simplify your answer.) 

Q:

Kovi has some toy cars. If he shares them with \(2\) or \(3\) friends, there will be no toy cars left. If he shares them with \(4\) friends, there will be \(1\) toy car left. What is the least possible number of toy cars he could have?

Q:

Kovi has some toy cars. If he shares them with \(2\) or \(3\) friends, there will be no toy cars left. If he shares them with \(4\) friends, there will be \(1\) toy car left. What is the least possible number of toy cars he could have?

Q:

You pick a card at random. What is \( P ( \) not even \( ) \) ? Write your answer as a percentage. 

Q:

 A store has caps on display. Five of the caps are red. There are \( 4 \) more blue caps than green caps. There are \( 3 \) fewer yellow caps than green caps. If there are \( 24 \) caps in all, how many caps are there of each color? 

Q:

In a \( 12 \) -sheet package of construction paper, there are \( 2 \) blue sheets. What is the probability that a randomly selected sheet will be blue? Write your answer as a fraction or whole number.

 

\( P ( \) blue \( ) = \) 

Q:

Which expression can you use to calculate the conditional probability of event \( A \) given that event \( B \) has occurred?

A. Which expression can you use to calculate the conditional probability of event A given that event B has occurred? \( P ( A ) + P ( B ) - P ( A \) and \( B )\) 

B. Which expression can you use to calculate the conditional probability of event \( A \) given that event \( B \) has occurred? \( P ( A ) \cdot P ( A | B )\) 

C. \(\frac{P(A\ \text{and}\ B)}{B}\)

D. \(\frac{P(A\ \text{and}\ B)}{A}\)

Q:

I. An apple bag contains \( 400 \) of apples in which \( 150 \) of them are green (G), \( 160 \) are red (R) and the rest of them are mixed colored (M). 

 

a) What is the probability that an apple will be mixed colored (M)? 

b) What is the probability that an apple will be red (R)? 

c) What is the probability that an apple will be green (G)? 

 

II. There are two scone machines called \( X \) and \( Y \) , work independently. \( X \) machine produces \( 3000 \) scones which \( 150 \) are damaged. \( Y \) machine produces \( 5000 \) of scones in which \( 250 \) are damaged. If one scone is taken out from each machine, what is the probability that BOTH scones are damaged? (Please provide the steps for calculations) 

 

III. At a supermarket, \( 65 \% \) of customers buy almond milk, \( 53 \% \) of them buy soya milk and \( 29 \% \) of them buy both almond and soya milk. Find out what proportion of customers buy at least one type of milk. (Please provide the steps for calculations) 

Q:

At a supermarket, \( 75 \% \) of customers buy brown bread, \( 65 \% \) buy white bread. If \( 50 \% \) of them buy both brown and white bread, what proportion of customers buy at least one kind of bread? (Please provide the steps for calculations) 

Q:

Consider a bag with marbles, 3 blue marbles, 4 red marbles, and 8 green marbles. Two marbles are drawn in sequence and are taken without replacement. What is the probability of taking a red marble and then a green marble?

A. \(\frac { 4 } { 5 } \)                B.\( \frac { 32 } { 225 } \)                   C. \( \frac { 16 } { 105 } \)                      D. \( \frac { 2 } { 5 }\) 

Q:

M&M plain candies come in a variety of colors. According to the M&M/Mars Department of Consumer Affairs the average distribution of colors in a bag of 100 candies is 30 brown, 20 yellow, 20 red, 10 orange, 10 green, and 10 blue. Suppose you have a bag of M&M candies and you take two candies at random, without replacing the first one. What is the probability or drawing an orange then a red?

Question \( 6 \) M\&M plain candies come in a variety of colors. According to the M\&M/Mars Department of Consumer Affairs the average distribution of colors in a bag of \( 100 \) candies is \( 30 \) brown, \( 20 \) yellow, \( 20 \) red, \( 10 \) orange, \( 10 \) green, and \( 10 \) blue. Suppose you have a bag of M\&M candies and you take two candies at random, without replacing the first one. What is the probability or drawing an orange then a red? 

A. \(\frac { 19 } { 1000 } \) 

B. \( \frac { 1 } { 50 } \) 

C. \( \frac { 1 } { 5 } \) 

D. \( \frac { 2 } { 99 }\) 

Q:

A bag contains 8 red marbles, 12 blue marbles, and 17 green marbles. If one marble is randomly selected from the bag, what is the probability that the marble is red or green?

 

\(\frac { 20 } { 37 } \) 

\( \frac { 8 } { 17 } \) 

\( \frac { 25 } { 37 } \) 

\( \frac { 29 } { 37 }\) 

Q:

A bag contains 8 red marbles, 12 blue marbles, and 17 green marbles. If one marble is randomly selected from the bag, what is the probability of not selecting a green marble?

\(\frac { 20 } { 37 } \) 

 

\( \frac { 17 } { 37 } \) 

\( \frac { 12 } { 37 } \) 

\( \frac { 8 } { 37 } \) 

\( \frac { 25 } { 37 }\) 

Q:

(a) Consider a \( t \) distribution with \( 13 \) degrees of freedom. Compute \( P ( - 1.35 < t < 1.35 ) \) . Round your answer to at least three decimal places. 

(b) Consider a \( t \) distribution with \( 22 \) degrees of freedom. Find the value of \( c \) such that \( P ( t \geq c ) = 0.05 \) . Round your answer to at least three decimal places. 

Q:

A cooler contains \( 66 \) cans of soda. There are \( 6 \) cans of cola, \(15 \) cans of orange soda, \( 24 \) cans of ginger ale, \(12 \) cans of root beer, and \( 9 \) cans of club soda. If one can of soda is randomly selected, determine the probability that the can is club soda. 

 

Q:

1. A bag of marbles has \( 8 \) red marbles and \( 6 \) purple marbles. Jennifer will randomly select \( 1 \) marble from the bag. What is the probability that she will NoT select a purple marble? 

A. \(3 / 4 \) 

B. \( 3 / 7 \) 

C. \( 4 / 7 \) 

D. \( 1 / 4\) 

 

2. What are the odd against pulling a purple marble? 

A. \(3 : 4 \) 

B. \( 4 : 3 \) 

C. \( 6 : 8 \) 

D. \( 8 : 6\) 

Q:

 Tara has a collection of small stuffed animals. She has \( 10 \) bears, \( 4 \) dogs, \( 4 \) cats, and \( 2 \) rabbits. Suppose Tara puts all her animals in a pillowcase and picks one without looking. Use a fraction to describe the probability that she will pick:

 

a) a bear b) a rabbit c) a dog 

Q:

A spinner has \( 5 \) sections of equal size labeled \( P , Q , R , S \) , and \( T \) . The arrow of this spinner is spun \( 15 \) times and landed \( 4 \) times on the section labeled Q. Which statement best describes the experimental probability and theoretical probability of the arrow landing on the section labeled Q?

A. The experimental probability is \( 4 / 15 \) , and the theoretical probability is \( 1 / 5 \) . 

B. The experimental probability is \( 1 / 5 \) , and the theoretical probability is \( 1 / 5 \) . 

C. The experimental probability is \( 4 / 15 \) , and the theoretical probability is \( 4 / 15 \) . 

D. The experimental probability is \( 1 / 5 \) , and the theoretical probability is \( 4 / 15 \) .  

 

Q:

A bag of candy contains \( 2 \) packs \( 1 \) point of Skittles, \( 4 \) Twizzlers, and \( 10 \) Reese's cups. What is the probability of reaching into the bag and choosing either a pack of Skittles or a Reese cup? 

A. \( 3 / 4 \) 

B. \( 3 / 8 \) 

C. \( 1 / 4 \) 

D. \( 1 / 8\) 

Q:

Alph played a two-dice game and \( 1 \) point recorded the following results: \( 2 \) , \( 2,8,12,10,6,4,8,6,2 \) . What is the experimental probability of rolling an \( 8 ? \) (Always reduce answers) 

A. \( 1 / 5 \) 

B. \( 2 / 10 \) 

C. \( 2 / 5 \) 

D. \( 1 / 10\) 

Q:

Suppose that each circle is equally likely to be selected. One circle is selected at random.Determine the probability indicated.Note that the symbols shown are black,red, or white. \(P(white - symbol| - symbol\ obtained)\)

Q:

A quality control inspector is checking a sample of lightbulbs for defects. The table summarizes the results. If one of these lightbulbs is selected at random, find the probability that the lightbulb is defective. 

\(\begin{array}{|c|c|c|c|} \hline \text{Wattage}&\text{Good}&\text{Defective}&\text{Total}\\ \hline 20&56&9&65\\ 50&66&8&74\\ 100&62&8&70\\ \text{Total}&184&25&209\\ \hline \end{array}\)

 

Q:

A quality control inspector is checking a sample of lightbulbs for defects. The table summarizes the results. If one of these lightbulbs is selected at random, find the probability that the lightbulb is good, given that it is \( 50 \) watts. 

      Wattage               Good               Defective              Total 

         \(20 \)                    58                      13                          71

         \( 50 \)                    59                      15                          74

        \( 100 \)                  73                       12                         85

        Total                  190                        40                       230

The probability is 

Q:

Of the graduating class of 96 high school students, 24 plan to attend university, 33 plan to attend college, and 19 plan to take an apprenticeship. The school surveys 25 at random. Show your work 

a) What is the probability that at least 3 people will be going into an apprenticeship? 

b) What is the probability that exactly 10 people will be going to college? 

c) What is the probability that of no one going to either of the 3 pathways? 

d) What is the expected value of people going to university

 

Q:

Tracy performed an experiment with a spinner. She spun the spinner and recorded the results in a frequency table. The spinner and the frequency table are given below. Find the experimental probability of the spinner landing on green or blue. 

\(\begin{array}{|c|c|c|c|c|} \hline \text{color}&\text{yellow}&\text{red}&\text{green}&\text{blue}\\ \hline \text{frequency}&6&4&7&3\\ \hline \end{array}\)

Write the probability as a fraction in the simplest form. 

Q:

Set up the problem as if it were to be solved, but do not solve. Assume that this selection is done without replacement. 

Determine the probability of being dealt \( 2 \) eights from a standard deck of \( 52 \) cards when \( 2 \) cards are dealt. 

Q:

Seven letters are to be selected at random from the English alphabet of \( 26 \) letters. Determine the probability that \( 7 \) consonants are selected.d. Assume there are \( 21 \) consonants in the alphabet and that selection is to be done without replacement. Set up the problem as if it were to be solved, but do not solve. 

Q:

A computer did a simulation of rolling a pair of dice \( 600 \) times. The sum of \( 7 \) was recorded by the computer a total of \( 112 \) times during this simulation. What was the difference in the theoretical probability of rolling a sum of \( 7 \) and the experimental probability of rolling a \( 7 \) for this simulation? 

Q:

\(16 \% \) of all Americans live in poverty. If \( 36 \) Americans are randomly selected, find the probability that 

a. Exactly \( 6 \) of them live in poverty. 

b. At most \( 4 \) of them live in poverty. 

c. At least \( 6 \) of them live in poverty. 

d. Between \( 6 \) and \( 11 \) (including \( 6 \) and \( 11 \) ) of them live in poverty. 

Round each answer to \( 4 \) decimal places. 

Q:

Mia owns a small business selling bagels. She knows that in the last week \( 85 \) customers paid cash, \( 5 \) customers used a debit cards, and \( 16 \) customers used a credit card. 

Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number. Answer: 

Q:

\(84 \% \) of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If \( 32 \) owned dogs are randomly selected, find the probability that 

a. Exactly \( 25 \) of them are spayed or neutered. 

b. At most \( 29 \) of them are spayed or neutered. 

c. At least \( 26 \) of them are spayed or neutered. 

d. Between \( 26 \) and \( 31 \) (including \( 26 \) and \( 31 \) ) of them are spayed or neutered. 

Round all answers to \( 4 \) decimal places. 

Q:

John spins a fair spinner with \( 5 \) equal sections numbered \( 1 \) through \( 5 \) . His spin lands on the number \( 2 \) . What is the probability that John's next three spins land on the number \( 2 \) ?

 A. \( \frac { 1 } { 25 } \) 

B. \( \frac { 1 } { 625 } \) 

C. \( \frac { 3 } { 125 } \) 

D. \( \frac { 1 } { 125 }\) 

Q:

Jane puts \( 2 \) sets of tiles in a bag. The tiles in each set are numbered \( 1 \) to \( 10 . \) She will select a tile from the bag, set it aside, then select again. What is the probability that Jane will select a \( 2 \) and then a \( 7 ?\) 

A. \( \frac { 1 } { 95 } \) 

B. \( \frac { 39 } { 190 } \) 

C. \( \frac { 7 } { 20 } \) 

D. \( \frac { 1 } { 11 }\) 

Q:

A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (or not). The data are in the table below. 

\(\begin{array}{|r|r|r|r|} \hline & \text { Completed HW } & \text { Did not Complete HW } & \text { Total } \\ \hline \text { Passed the Course } & 26 & 7 & 33 \\ \hline \text { Did not Pass the Course } & 3 & 18 & 21 \\ \hline \text { Total } & 29 & 25 & 54 \\ \hline \end{array}\)

A student from the class is randomly selected. Determine the following probabilities. Enter your results as percentages rounded to two decimal places. 

 

1. What is the probability a student passed the course? 

 

2. What is the probability a student passed the course or completed the HW? 

 

3. What is the probability a student passed the course and completed the HW? 

 

4. What is the probability a student completed their homework given that they passed the course? 

 

Q:

The clients who get haircuts at Austin's salon have a variety of hair colours. 

\(\begin{array}{|l|l|} \hline \text { blond } & 4 \\ \hline \text { red } & 7 \\ \hline \text { black } & 5 \\ \hline \end{array}\) 

What is the experimental probability that the next client to get a haircut Austin's salon will have blond hair? 

Q:

The local weather station reports that the chance of sleet is \( 0.12 \) . Write this probability as a fraction and as a percent. 

\( 3 / 25,12 \% \) 

\( 6 / 25,12 \% \) 

\( 44 / 25,88 \% \) 

\( 22 / 25,88 \% \) 

Q:

When Amy chooses a marble from a bag, there is a \( 16 \% \) chance that it will be a white marble, a \( 28 \% \) chance that it will be a blue marble, a \( 16 \% \) chance that it will be a green marble, and a \( 40 \% \) chance that it will be a yellow marble. Which colors have equal probability? 

blue and white 

white and green 

green and yellow 

Cannot be determined. 

Q:

A special deck of cards has \( 5 \) green cards, and \( 3 \) yellow cards. The green cards are numbered \( 1,2,3,4 \) , and \( 5 \) . The yellow cards are numbered \( 1,2 \) , and \( 3 \) . The cards are well shuffled and you randomly draw one card. 

\( G = \) card drawn is green 

\( E = \) card drawn is even-numbered

 a. How many elements are there in the sample space?

 b. \( P ( E ) = \square \) (Round to \( 4 \) decimal places) 

Q:

Thomas wants to invite Madeline to a party. He has an \( 80 \% \) chance of bumping into her at school. Otherwise, he'll call her on the phone. If he talks to her at school, he's \( 90 \% \) likely to ask her to a party. However, he's only \( 60 \% \) likely to ask her over the phone. 

This is the tree diagram that represents the probability of Thomas inviting Madeline to a party.

 

What is the probability of Thomas inviting Madeline to the party over the phone? 

A. \(20 \% \) 

B. \( 80 \% \) 

C. \( 60 \% \) 

D. \( 12 \% \) 

Q:

Thomas wants to invite Madeline to a party. He has an \( 80 \% \) chance of bumping into her at school. Otherwise, he'll call her on the phone. If he talks to her at school, he's \( 90 \% \) likely to ask her to a party. However, he's only \( 60 \% \) likely to ask her over the phone. This is the tree diagram that represents the probability of Thomas inviting Madeline to a party. 

What is the total probability of Thomas inviting Madeline to the party? 

\( 84 \% \) 

\( 100 \% \) 

\( 90 \% \) 

\( 64 \% \) 

Q:

A box holds \( 2 \) pens, \( 2 \) pencils and \( 1 \) highlighter. Tim picks one item, a pen, and does not return it to the box. He then picks a second item. 

What is the probability that the second item is a pencil? 

\(20 \% \)

\(25 \% \)

\(80 \% \)

\(50 \% \)

Q:

Suppose that in a certain country the heights of the adult females is normally distributed with a mean of \(165 cm \) and a standard deviation of \( 7 cm \) . If there are \( 5000000 \) adult females in the country, 

What percentage of the females are shorter than \( 172 cm \) ?

What percentage of the females are taller than \(151cm\) ?

What percentage of the females have heights between \( 158 cm \) and \( 179 cm \) ? 

How many of the females are shorter than \( 151 cm \) ? 

How many of the females are between \( 151 cm \) and \( 179 cm \) ? 

Q:

 

1. A light bulb manufacturer claims that the lifetime of the bulbs is normally distributed with a mean of  

\( 5000 \) hours and \( 2 \) standard deviation of \( 250 \) hours. If \( 20000 \) bulbs are produced on a particular day, 

(d) How many of the \( 20000 \) bulbs will last less than \( 4250 \) hours? 

(e) How many of the \( 20000 \) bulbs will last more than \( 5250 \) hons? 

Q:

At Daisy Donuts, \( 6 \) of the last \( 14 \) donuts sold had sprinkles. What is the experimental probability that the next donut sold will have sprinkles? Simplify your answer and write it as a fraction or whole number. 

Q:

A factory inspector found flaws in \( 4 \) out of \( 20 \) wooden boxes. What is the experimental probability that the next wooden box will be flawed? Simplify your answer and write it as a fraction or whole number. 

\( P ( \) flawed box \( ) = \) 

Q:

Terrence is recording what kind of shoes people are wearing at the mall. Out of the \( 20 \) people he has seen, \( 8 \) are wearing high heels. What is the experimental probability that the next person Terrence sees will be wearing high heels? Simplify your answer and write it as a fraction or whole number. 

\( P ( \) high heels) 

Q:

Angie surveyed some students at her school about their favourite professional sports. Of the students surveyed, \( 3 \) said baseball was their favourite sport, while \( 3 \) of the students had other favourite sports. What is the experimental probability that the next student Angie talks to will pick baseball? 

Simplify your answer and write it as a fraction or whole number. 

\( P ( \) baseball) \( = \square\) 

Q:

Jon works at an appliance store. He recently sold \( 20 \) appliances, \( 4 \) of which were dishwashers. What is the experimental probability that the next appliance Jon sells will be a dishwasher? 

Simplify your answer and write it as a fraction or whole number. 

Q:

Bella gets \( 8 \) heads when flipping a weighted coin \( 10 \) times. What is the experimental probability that the next flip will come up heads? 

Q:

Students in a communications course are required to start a blog on a topic of their choice. Of the students who have already begun, \( 25 \) of them are writing about news, while \( 55 \) of them are writing about other topics. What is the experimental probability that the next blog started will be about news? 

Q:

A miniature golf course recently provided its customers with \( 44 \) golf balls, of which \( 10 \) were purple. What is the experimental probability that the next customer will receive a purple golf ball? 

\( P ( \) purple) \( = \square\) 

Q:

A miniature golf course recently provided its customers with \( 44 \) golf balls, of which \( 10 \) were purple. What is the experimental probability that the next customer will receive a purple golf ball? 

Q:

You pick a card at random. What is \( P ( \) odd or factor of \( 36 ) ? \) 

Write your answer as a percentage. 

Q:

What is the probability that a standard number cube will show a one, two, five, or six when it is rolled? Write the probability as a fraction in simplest form. 

 

Q:

Two fair dice are rolled. 

Find the odds for and the odds against getting the same number twice. 

The odds for getting the same number twice are ______ to _______(Simplify your answers. Type whole numbers.) 

The odds against getting the same number twice are ______ to ______(Simplify your answers. Type whole numbers.) 

Q:

Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or estimate the following probability. What is the probability of not hearing your favorite group on a random shuffle of your playlist that has \( 1572 \) songs, of which \( 131 \) are by your favorite group? Which method is appropriate? 

The subjective method 

The theoretical method

The relative frequency method 

The probability is 

Q:

Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or estimate the following probability. 

Randomly meeting someone whose Social Security number ends in the same digit as yours 

Choose the correct answer below. 

A. Using the theoretical method, the probability is \( \frac { 1 } { 10 } \) . 

B. Using the relative frequency method, the probability is \( \frac { 1 } { 10 }\) .

C. Using the subjective method, the probability is \( \frac { 1 } { 10 } \) . 

D. Using the relative frequency method, the probability is \( 0.9 \) . 

E. Using the subjective method, the probability is \( 0.9 .\) 

F. Using the theoretical method, the probability is \( 0.9 .\) 

Q:

Determine whether the following individual events are overlapping or non-overlapping. Then find the probability of the combined event. Drawing either a black four or a red king on one draw from a regular deck of cards 

 

Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. (Type an integer or a simplified fraction.)

A. The individual events are non-overlapping. The probability of the combined event is  

B. The individual events are overlapping. The probability of the combined event is 

Q:

Use the method of your choice to determine the following probability. Drawing three fives in a row from a standard deck of cards when the drawn card is not returned to the deck each time 

 

The probability of drawing three fives is 

(Type an integer or a simplified fraction.) 

Q:

A ball is drawn randomly from a jar that contains \( 3 \) red balls, \( 9 \) white balls, and \( 2 \) yellow balls. Find the probability of the given event. Write your answers as reduced fractions or whole numbers.

(a) \( P ( \) A red ball is drawn) 

(b) \( P ( \) A white ball is drawn)

(c) \( P ( \) A yellow ball is drawn) 

(d) \( P ( \) A green ball is drawn) 

Q:

The letters in the word CALCULATE are arranged randomly. Write your answers in decimal form. Round to the nearest thousandth as needed. What is the probability that the first letter is U? What is the probability that the first letter is \( C \) ? What is the probability that the first letter is a vowel? What is the probability that the first letter is H?  

Q:

A card is drawn randomly from a standard \( 52 \) -card deck. Find the following: Write all answers as simplified fractions (not mixed numbers).

Probability the card drawn is a face card

Probability the card drawn is not a face card. 

Odds in favor of drawing a face card 

Odds against drawing a face card 

Q:

The weatherman says that there is a \( 72 \% \) chance of rain today. What is the probability that it will not rain today? What are the odds that it will rain today? Simplify your answers and round to the nearest hundredth as needed.  

Q:

Kent flips a coin and rolls a standard number cube. Find the probability that the coin will show heads and the cube will show eight. Write the probability as a fraction in simplest form. 

Q:

What type of test: A drug company claims that an allergy medication causes headaches in \( 5 \% \) of those who take it. A medical researcher believes that more than \( 5 \% \) of those who take the drug actually get headaches. 

a) What kind of hypothesis test is this? 

A. single-mean t distribution 

B. two-means (paired) t distribution 

C. two-proportions normal distribution 

D. two-means (unpaired) t distribution 

E. single-proportion normal distribution 

 

b). Which hypotheses do we want to test? 

A. \(H _ { 0 } : p _ { 1 } = 0.05 \) 

    \( H _ { A ^ { * } } : p _ { 1 } = 0.05\) 

B. \(H _ { 0 } : p _ { 1 } = 0.05 \) 

    \( H _ { A } : p _ { 1 } = 0.05\) 

C. \(H _ { 0 } : P _ { 1 } = 0.05 \) 

    \( H _ { A } : P _ { 1 } < 0.05\) 

D. \(H _ { 0 } : P _ { 1 } = 0.05 \) 

    \( H _ { A} : p _ { 1 } > 0.05\) 

Q:

Definition: Which of the following is the best definition of the \( p \) -value? 

A. The probability of observing a sample at least as favorable to \( H _ { a } \) as our sample, under the assumption that \( H _ { 0 } \) is true. 

B. The probability of observing our sample if \( H _ { 0 } \) is true. 

C. The probability of rejecting \( H _ { 0 } \) 

D. The probability that \( H _ { 0 } \) is true. 

Q:

A college professor asked his psychology students to complete a personality test. He  special attention to his students' career goals and their greatest fears. What is the probability that a randomly selected student wants to be a therapist or psychiatrist? Simplify any fracyions.

Q:

An ordinary (fair) die is a cube with the numbers \( 1 \) through \( 6 \) on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event \( A \) : The sum is greater than \( 9 \) . Event \( B \) : The sum is not divisible by \( 2 \) and not divisible by \( 3 \) . Round your answers to two decimal places. (a) \( P ( A ) = \)

(b) \( P ( B ) = \) 

Q:

\(\left. \begin{array} { l } { \text { The probability that a student at your school takes Drivers Education and } } \\ { \text { Spanish is } \frac { 87 } { 1000 } \text { . The probability that a student takes Spanish is } \frac { 68 } { 100 } \text { . } } \\ { \text { What is the probability that a student takes Drivers Ed given that the } } \\ { \text { student is taking Spanish? Enter your answer as a reduced fraction using / } } \\ { \text { for the fraction bar. Do not use any spaces in your answer. } } \\ { \text { The probability that a student takes Drivers Education given that the } } \\ { \text { student is taking Spanish is } } \end{array} \right.\)

The probability that a student at your school takes Drivers Education and Spanish is \( \frac { 87 } { 1000 } \) . The probability that a student takes Spanish is \( \frac { 68 } { 100 } \) . What is the probability that a student takes Drivers Ed given that the student is taking Spanish? Enter your answer as a reduced fraction using / for the fraction bar. Do not use any spaces in your answer. The probability that a student takes Drivers Education given that the student is taking Spanish is 

Q:

A committee of \( 4 \) is being formed randomly from the employees at a school: \( 4 \) administrators, \( 32 \) teachers, and \( 4 \) staff. What is the probability that all \( 4 \) members are teachers? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. 

Q:

A box of jerseys for a pick-up game of basketball contains \( 9 \) extra-large jerseys, \( 6 \) large jerseys, and \( 4 \) medium jerseys. If you are first to the box and grab \( 3 \) jerseys, what is the probability that you randomly grab \( 3 \) large jerseys? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. 

Q:

A box of jerseys for a pick-up game of basketball contains \( 8 \) extra-large jerseys, \( 6 \) large jerseys, and \( 3 \) medium jerseys. If you are first to the box and grab \( 3 \) jerseys, what is the probability that you randomly grab \( 3 \) large jerseys? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. 

 

Answer 

Q:

A committee of \( 3 \) is being formed randomly from the employees at a school: \( 5 \) administrators, \( 34 \) teachers, and \( 4 \) staff. What is the probability that all \( 3 \) members are administrators? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. 

 

Answer

Q:

Find the probability of choosing a letter other than the letter U from a bag that contains the nineteen letters of the French city BOULOGNE-BILLANCOURT. 

Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. Answer 

Q:

It is presentation day in class and your instructor is drawing names from a hat to determine the order of the presentations. If there are \( 19 \) students in the class, what is the probability that the first \( 3 \) presentations will be by Mila, Todd, and Kelly, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

 Answer 

 

Q:

The amount of time to complete a physical activity in a PE class is approximately normally distributed with a mean of \( 32 \) seconds and a standard deviation of \( 6.8 \) seconds: a) What is the probability that a randomly chosen student completes the activity in less than \( 24.5 \) seconds? 

\( 0.1357 \) 

b) What is the probability that a randomly chosen student completes the activity in more than \( 35.9 \) c) What proportion af students take between \( 27 \) and \( 37.4 \) seconds to complete the activity? \( - 0.73529 \) 

d) \( 70 \% \) of all students finish the activity in less than \( 35.6 \) seconds. 

Q:

There are \( 11 \) balls numbered \( 1 \) through \( 11 \) placed in a bucket. What is the probability of reaching into the bucket and randomly drawing two balls numbered \( 1 \) and \( 4 \) without replacement, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.  

Q:

A bex contains nine cards labeed \( J , K , L , M , N , O , P , Q \) , and \( R \) . One card will be randomly chosen. What is the probability of choosing a letter from \( K \) to \( Q \) ? wrte your answer as a fraction. 

Q:

Ten balls numbered from \( 1 \) to \( 10 \) are placed into a bag. Some are grey and some are white. The balls numbered \( 1,2,3,4,6,7,8 \) , and \( 10 \) are grey. The balls numbered \( 5 \) and \( 9 \) are white. A ball is selected at random. Let \( X \) be the event that the selected ball is white, and let \( P ( X ) \) be the probability of 

\( X \) . Let not \( X \) be the event that the selected ball is not white, and let \( P ( \) not \( X ) \) be the probability of not \( X \) . 

(a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. 

Q:

An ordinary (fair) die is a cube with the numbers \( 1 \) through \( 6 \) on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.

Compute the probability of each of the following events. 

      Event \( A \) : The sum is greater than \( 5 \) . 

      Event B: The sum is an even number. 

Round your answers to two decimal places. 

Q:

The measurement of the circumference of a circle is found to be \( 68 \) centimeters, with a possible error of \( 0.9 \) centimeter. 

(a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places.) 

(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed \( 2 \% \) . (Round your answer to one decimal place.) 

 

Q:

There are \( 11 \) balls numbered \( 1 \) through \( 11 \) placed in a bucket. What is the probability of reaching into the bucket and randomly drawing four balls numbered \( 1,8,11 \) , and 

\( 5 \) without replacement, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. 

Q:

Of the people who fished at Clearwater Park today, 36 had a fishing license, and 24 did not. Of the people who fished at Mountain View Park today, 35 had a license, and 15 did not. ( no one fished at both parks). Suppose that one fisher from each park is chosen at random. What is the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license? Do not round your answer.

Of the people who fished at Clearwater Park today, \( 36 \) had a fishing license, and \( 24 \) did not. Of the peopl license, and \( 15 \) did not. (No one fished at both parks.) Suppose that one fisher from each park is chosen at random. What is the probability that the fisher chose chosen from Mountain View did not have a license? Do not round your answer. 

Q:

 Assume that when adults with smartphones are randomly selected, \( 58 \% \) use them in meetings or classes. If \( 5 \) adult smartphone users are randomly selected, find the probability that at least \( 2 \) of them use their \( 5 \) , \( 5.2 .23 \) - \( 7,18.75 \) of \( 32 \) points smartphones in meetings or classes. 

The probability is \( \square \) . (Round to four decimal places as needed.) 

Q:

The producer of a welght-loss pll advertises that people who use the pill lase, after one week, an average (mean) of \( 1.75 \) pounds with a standard devlation of \( 1.02 \) pounds. In a recent study, a group of \( 50 \) pcople who used this pill were intervlewed. The study revealed that these people lost a mean of \( 1.88 \) pounds after one week. 

If the producer's claim is correct, what is the probability that the mean wcight loss aftcr ane week an this pill for a random sample of \( 50 \) Individuals will be I. 88 pounds or more? 

Carry your intermediate computations to at least four decimal places, Round your answer to at least three decimal places. 

Q:

A multiple-cholce examination consists of \( 85 \) questlons, each having possible cholces a, b, c, d, and e. Approximate the probability that a student will get at least \( 20 \) answers correct if she randomly guesses at cach answer. (Note that, If she randomly guesses at each answer, then the probability that she gets any one answer correct is \( 0.2 \) .) Use the normal approximation to the binomial with a correction for continulty. Round your answer to at least three decimal places. Do not round any intermedlate steps. (If necessary, consult a llst of formulas.) 

Q:

The mean starting salary offered to graduating students with a ccrtain major in a recent year was \( \$ 64,215 , \) with a standard deviation of \( \$ 3678 \) . A random sample of \( 80 \) of that year's graduating students with the major has been selected. What Is the probability that the mean starting salary offered to these \( 80 \) students was \( \$ 64,750 \) or more? Carry your Intermediate computations to at least four decimal places, Round your answer to at least three decimal places. 

Q:

According to the records of a soft drink company, the bottles for their onc-liter-slzcd products contaln an average (mean) of I.02 liters of beveragc, with a standard deviation of \( 0.14 \) liters. As part of routinc quality assurance, a sample of \( 50 \) bottles has been taken. The sample mean amount of beverage in these \( 50 \) bottles was \( 0.995 \) liters. Assuming the company's records are correct, find the probability of observing a sample mean of \( 0.995 \) liters or less in a sample of \( 50 \) botties. Carry your Intermedlate computations to at least four decimal places. Round your answer to at least three decimal places. 

Q:

A bag of \( 13 \) marbles contains \( 5 \) marbles with red on them, \( 5 \) with blue on them, \( 6 \) with green on them, and \( 4 \) with red and green on them. What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. 

Q:

Suppose that \( 12 \% \) of the population of the U.S. is left-handed. If a random sample of \( 190 \) people from the U.S. is chosen, approximate the probability that fewer than \( 19 \) are left-handed. Use the normal approximation to the binomial with a correction for continuity. 

Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.) 

Q:

Suppose that \( 17 \% \) of the people in a large city have used a hospital emergency room in the past year. If a random sample of \( 160 \) people from the city is taken, approximate the probability that at least \( 25 \) used an emergency room in the past year. Use the normal approximation to the binomial with a correction for continulty. 

Round your answer to at least thrce decimal places. Do not round any intermediate steps. (If necessary, consult a llst of formulas.) 

Q:

The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) Is \( 1 \% \) , The manufacturer's control department periodically tests samples of the bulbs, and when \( 1.25 \% \) or more are defective, they call repair technicians for service. 

The control department is golng to take a random sample of \( 4400 \) light bulbs. Let \( \hat { p } \) be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. 

Answer the following. (if necessary, consult a list of formulas.) 

(a) Find the mean of \( \hat { p } \) . 

 

(b) Find the standard deviation of \( \hat { p } \) . 

 

(c) Compute an approximation for \( p ( \hat { p } \geq 0.0125 \) ), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places. 

Q:

Brandi has equal numbers of hip-hop songs and country songs loaded on her personal music player. She has it set to play songs on a random shuffle. Suppose Brandi is designing a simulation that could be used to estimate the probability that the next three songs to play are all hip-hop songs. 

Which simulation design could Brandi use to estimate the probability? 

A. Number cube 

     Let \( 1 = \) hip-hop 

     Let \( 2 = \) country 

     Roll cube three times. Repeat. 

B. Random digits 

     Let \( 0,1 = \) hip-hop 

     Let \( 2,3,4,5,6 = \) country 

     Select two random digits. Repeat. 

C. Number cube 

     Let \( 1 = \) hip-hop 

     Let \( 2 = \) country 

     Roll cube four times. Repeat. 

D. Coin 

     Let heads \( ( H ) = \) hip-hop 

     Let tails \( ( T ) = \) country 

     Toss coin three times. Repeat. 

 

Q:

Theoretical probability helps us know how likely an event is to occur. Which of the following

probabillties would tell us that the event is verY LIKELY to occur?

 A. A probability that is close to \( 0 \) , such as \( 1 / 100 \) 

B. A probability of \( 1 / 2 \) such as \( 50 / 100 \) 

C. A probability that is close to \( 1 \) , such as \( 99 / 100\) 

Q:

An ordinary (fair) die is a cube with the numbers \( 1 \) through \( 6 \) on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event \( A \) : The sum is greater than \( 6 \) . Event B: The sum is an odd number. 

(a) \( P ( A ) = \prod \) 

(b) \( P ( B ) = \square\) 

Q:

In a study of helicopter usage and patient survival, among the \( 41,123 \) patients transported by helicopter, \( 268 \) of them left the treatment center against medical advice, and the other \( 40,855 \) did not leave against medical advice. If \( 40 \) of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left the treatment center against medical advice? 

Q:

An ordinary (fair) die is a cube with the numbers \( 1 \) through \( 6 \) on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event \( A \) : The sum is greater than \( 8 \) . Event \( B \) : The sum is an even number. Write your answers as fractions.

Q:

A Prodigiks laptop is sold for \( \$ 1,189 \) at a reduction of \( 18 \% \) on its recommended retail price. What was the co nputer's initial (recommended retail) price? Round your answer to the nearest dollar. 

Q:

The average price of a \( P C \) is \( \$ 949 \) . If the computer prices are approximately normally distributed with standard deviation of \( \$ 100 \) , what is the probability that a randomly selected \( P C \) costs more than \( \$ 1200 ? \) 

A. \( 6 \% \) 

B. \(0 .9940 \) 

C. \(0 .006 \) 

D. \(0 .4940\) 

Q:

The GPA at the BEST UNIVERSITY has a normal distribution with a mean \( 2.46 \) and standard deviation \( 1.13 . \) Approximatelly what percent of the BEST UNIVERSITY students have their GPA below \( 1.54 \) . 

\( 79.1 \% \) 

\( 20.9 \% \) 

\( 71 \% \) 

\( 29.1 \% \)