The star basketball player at your high school claims to make 50% of his three-point shots. Recently, he missed 7 of his first 10 three-point shots. Is this surprising for this player? Assume that the player is, in fact, able to make 50% of his three-point shots. We need to carry out a simulation to estimate the probability that he would miss 7 or more of his first 10 three-point shots. Here are the results of 100 simulated trials. Which of the following answers the question of interest?
Answer
A
The player’s true three-point success rate is actually only 18%, according to this simulation.
B
Based on the 100 simulated trials, there is about an 18% chance of the player missing 7 of his first 10 three-point shots. This probability is not unusually low, so it is not unlikely.
C
Based on the 100 simulated trials, it is more likely that the player would make 5 or 6 out of every 10 three-point shots.
D
In a very long series of trials, this player should make approximately 50% of his shots. He must have been having an off day.
Explanation
If he makes 50% of his shots, he also misses 50% on each shot. The simulation estimates how often he would miss at least 7 of 10; about 18% of the 100 trials did so. That is not an unusually small probability, so missing 7 of his first 10 shots is not especially surprising. Choice B gives this interpretation; the simulation does not show that his true success rate is 18%.
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