Question

a spinner with 5 equally sized slices has 3 red slices, 1 yellow slice, and 1 blue slice. maya spun the dial 20 times and got the following results.

outcome	red	yellow	blue

answer the following. round your answers to the nearest thousandths.
(a) from mayas results, compute the experimental probability of landing on yellow.
(b) assuming that the spinner is fair, compute the theoretical probability of landing on yellow.
(c) assuming that the spinner is fair, choose the statement below that is true.

• the experimental and theoretical probabilities must always be equal.
• as the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
• as the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.

Explanation:

Step1: Calculate experimental yellow probability

$\text{Experimental Probability} = \frac{\text{Yellow spins}}{\text{Total spins}} = \frac{5}{20} = 0.250$

Step2: Calculate theoretical yellow probability

$\text{Theoretical Probability} = \frac{\text{Yellow slices}}{\text{Total slices}} = \frac{1}{5} = 0.200$

Step3: Identify true probability statement

Match to law of large numbers.

Answer:

(a) $0.250$
(b) $0.200$
(c) As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.