Question

a spinner with 10 equally sized slices has 5 yellow slices, 3 red slices, and 2 blue slices. mary spun the dial 20 times and got the following results.

outcome	yellow	red	blue

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

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

Explanation:

Step1: Calculate experimental blue probability

$\text{Experimental Probability} = \frac{\text{Blue Spins}}{\text{Total Spins}} = \frac{2}{20} = 0.100$

Step2: Calculate theoretical blue probability

$\text{Theoretical Probability} = \frac{\text{Blue Slices}}{\text{Total Slices}} = \frac{2}{10} = 0.200$

Step3: Identify true probability statement

Use law of large numbers principle.

Answer:

(a) $0.100$
(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.