Question

the spinner below shows 10 equally sized slices. jessica spun the dial 20 times and got the following results.

outcome	grey	white	black

fill in the table below. round your answers to the nearest thousandth.

(a) from jessicas results, compute the experimental probability of landing on grey or black.

(b) assuming that the spinner is fair, compute the theoretical probability of landing on grey or black.

(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.
• as the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.
• the experimental and theoretical probabilities must always be equal.

Explanation:

Step1: Calculate experimental probability

Experimental probability = (grey + black spins)/total spins = (8+3)/20 = 11/20 = 0.550

Step2: Calculate theoretical probability

Theoretical probability = (grey + black slices)/total slices = 5/10 = 0.500

Step3: Choose correct statement

By the law of large numbers, experimental probability approaches theoretical as trials increase.

Answer:

0.550
0.500
As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.