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Marlena has a bag of coins. The bag contains 8 quarters, 10 dimes, 4 nickels, and 2 pennies. She will randomly select a coin from the bag. What is the probability that Marlena will select a nickel?


A.\(\frac{1}{12}\)     B.\(\frac{1}{3}\)     C.\(\frac{1}{6}\)     D.\(\frac{1}{5}\)


4) For lunch at school, you get 3 choices for the main food item, 2 choices of fruit, 2 choices for vegetable, and 3 choices for drink. Use the Fundamental Counting Principle to find how many . different possible outcomes (lunch combinations) you have to choose from. Show your work. 


a) 1 lunch combination        b) 18lunch combinations    c) 36 lunch combinations


A carnival roulette wheel contains \(22\) slots numbered \(00\)\(0\)\(1\)\(2\)\(3\), ..., \(20\)\(10\) of the slots numbered \(1\) through \(20\) are colored red, and \(10\) are colored black. and \(10\) are colored black. The \(00\) and \(0\) slots are uncolored. The wheel is spun, and a ball is rolled around the rim until it falls into a slot. What is the probability that the ball falls into a black or red slot.


Event \(\mathrm{A}\) and \(\mathrm{B}\) are independent. Find the indicated Probability.


\(P(B)=\fbox{\phantom{?????????}}\) (round answer to three decimal places)



A pizza shop has available toppings of anchovies, mushrooms, peppers, onions, olives, bacon, pepperoni and sausage. How many different ways can a pizza be made with \(4\) toppings.


Gwen has two boxes of accessories. One contains scarfs and the other contains gloves. The probability of her selecting a red scarf from the first box is 3/4 and the probability of her selecting a pair of golden gloves from the other box is 1/4. Gwen is getting ready to go out, what is the probability that Gwen selects a red scarf from the first box and a pair of golden gloves from the second box? 


Two marbles are drawn randomly one after the other without replacement from a jar that contains \(7\) red marbles, \(8\) white marbles, and \(9\) yellow marbles. Find the probability of the following events.


(a) A red marbles is drawn first followed by a white marble.

(b) A white marble is drawn first followed by a white marble.

(c) A yellow marble is not drawn at all.


Are the sets equal?


\(\mathrm{A}=\{15, 16, 16, 17, 17, 17, 18, 18, 18, 18\}\)

\(\mathrm{B}=\{18, 17, 17, 15\}\)


In a survey of a group of people, it was found that \(60\%\) of the people liked apple, \(70\%\) liked orange and \(400\) people liked both of them. If \(10\%\) people liked non of them, then


(i) Represent the above information in a Venn-diagram

(ii) Find the total number of people in the survey

(iii) Find the number of people who like apple only. 


Suppose we want to choose \(6\) objects, without replacement, from \(15\) distinct objects. 


(a) How many ways can this be done, if the order of the choices does not matter?

(b) How many ways can this be done, if the order of the choices matters?