Question

experimental and theoretical probability
a spinner below shows 10 equally sized slices. kira spun the dial 1000 times and got the following results.

outcome	grey	white	black

fill in the table below. round your answers to the nearest thousandth.
(a) assuming that the spinner is fair, compute the theoretical probability of landing on white or grey.

(b) from kiras results, compute the experimental probability of landing on white or grey.

(c) assuming that the spinner is fair, choose the statement below that is true:

• with a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.
• with a large number of spins, there must be no difference between the experimental and theoretical probabilities.

Explanation:

Step1: Count white/grey slices

Count of white/grey slices: $5 + 3 = 8$
Total slices: $10$

Step2: Calculate theoretical probability

$\text{Theoretical Probability} = \frac{8}{10} = 0.800$

Step3: Sum white/grey experimental spins

Total white/grey spins: $507 + 290 = 797$
Total spins: $1000$

Step4: Calculate experimental probability

$\text{Experimental Probability} = \frac{797}{1000} = 0.797$

Step5: Identify valid probability statement

Law of Large Numbers: large trials mean small, possible difference.

Answer:

(a) $0.800$
(b) $0.797$
(c) With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.