Question

Kayleigh has a spinner with sections labeled A‒E. All sections are the same size. She spins it 20 times with outcomes as follows:

Outcome Number of Times
A 4
B 4
C 5
D 5
E 2
a) Find the theoretical probability that the spinner lands on A or E. b) Find the experimental probability that the spinner lands on A or E. c) Explain why the probabilities are different.

Answer 1

Answer A or E he size spin 20 times than the others

Answer 2

a) The theoretical probability of landing on A or E is 2/5. This is because there are two sections we want to land on (either A or E) out of 5 sections total.

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b) The empirical probability of landing on A or E is 3/10, which was reduced from 6/20. This is because there are 4+2 = 6 times we landed on either A or E out of 20 spins total.

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c) Due to the nature of random events, the theoretical and empirical probabilities will not match up perfectly (basically every random experience will be different for each person). This is especially true for small sample sizes. However, as you do more spins, you should find that the empirical probabilities will slowly approach the theoretical probability. The theoretical probability is always going to be 2/5 for this problem; while the empirical probabilities will bounce around because of the nature of random chance.