Shamir loves watching professional basketball. His favorite player, Freddy Rocket, successfully completes 85 percent of his free throws. During one game, Rocket misses his first four free throws. Shamir says that the next free throw has to be a success since Rocket rarely misses so many in a row. Is Shamir’s reasoning correct?
Answer
A
Yes, Rocket missed the first four free throws, so the fifth one is due to be a success.
B
No, it is very unlikely for Rocket to miss so many free throws in a row, so Shamir should expect the player to continue missing baskets.
C
No, the probability of Rocket making a free throw is 0 point 8 5 over the long run.
D
Yes, Rocket has a high probability of making free throws, so the next one must go in the basket.
Explanation
Shamir’s reasoning is not correct because previous free throws do not make the next one “due” to go in. If each attempt has the same chance of success, Rocket’s probability of making the next free throw is still 0.85 (85%), even after four misses. Choice C correctly describes this probability over the long run; it does not guarantee the outcome of any single shot.
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