Question

a spinner with 10 equally sized slices has 5 yellow slices, 3 red slices, and 2 blue slices. maria spun the dial 100 times and got the following results.

outcome	yellow	red	blue

answer the following. round your answers to the nearest thousandths.
(a) from marias 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

$\text{Experimental Probability} = \frac{\text{Yellow Spins}}{\text{Total Spins}} = \frac{60}{100} = 0.600$

Step2: Calculate theoretical yellow probability

$\text{Theoretical Probability} = \frac{\text{Yellow Slices}}{\text{Total Slices}} = \frac{5}{10} = 0.500$

Step3: Identify true probability statement

Match to the law of large numbers principle.

Answer:

(a) $0.600$
(b) $0.500$
(c) As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.