\(P( purple) = \frac { 8} { 41} = 0.20\)

UpStudy Free Solution By Steps

Step 1: Determine the total number of spins

- Add the frequencies of all the colors to find the total number of spins.

\[\text { Total spins} = 7 + 15 + 6 + 5 + 8\]

\[\text { Total spins} = 41\]

Step 2: Find the frequency of purple

- The frequency of purple is given as 8.

Step 3: Calculate the probability of landing on purple

- The probability \(P\) of an event is given by the ratio of the frequency of the event to the total number of outcomes.

\[P( \text { Purple} ) = \frac { \text { Frequency of Purple} } { \text { Total spins} } \]

\[P( \text { Purple} ) = \frac { 8} { 41} \]

Step 4: Convert the fraction to a decimal

- Perform the division to get the decimal value.

\[P( \text { Purple} ) \approx \frac { 8} { 41} \approx 0.1951\]

Step 5: Round to the nearest hundredth

- Round 0.1951 to the nearest hundredth.

\[P( \text { Purple} ) \approx 0.20\]

Key Concepts:

1. Probability: Strictly speaking, probability is a measure of the likelihood of any event to happen; it is computed with the ratio of numbers of favorable outcomes to the total possible number of outcomes.

2. Frequency: Frequency is the number of occurrences of an event concerning the time in a particular number of observations or experiments.

With a reasonable understanding of these ideas, you should be capable of calculating the probabilities correctly. This is one of the most essential skills covered in virtually any course that introduces probability and statistics. If you need homework assistance with your assignment questions, give the creation of a step-by-step solution a try using Upstudy AI Homework Solver. UpStudy ensures you are crystal clear with every concept through our solution explanations and personal support. Learn with UpStudy now!