Brain Buster Answers

Brain Buster #1

The probability that a player will make only one free throw is slightly more than 4/25. If he makes his first free throw (probability 4/5) and misses his second free throw (probability 1/5), we get a compound probability of (4/5)*(1/5) = 4/25. But if he missed the first free throw he will most likely try to intentionally miss the second free throwso that he or a teammate can put in the rebound. There is no sense in making the second free throw in that case because the opponent would then have the ball with a one-point lead with only 1.7 seconds left on the clock. The reason the final probability is slightly more than 4/25 is that the player, in deliberately trying to miss the second free throw might screw up and accidentally make it.

     From Sit and Solve Brainteasers by Derrick Niederman

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One response to “Brain Buster Answers

  1. Dave

    That assumes that a player who makes 80% of FTA shoots them independently. I don’t think this assumption is valid, in fact your answer argues that this is not the case in this special context.
    Is it not possible that a player (empirically observed) shoots the first FT at 70-75%, but the second at ~90% when they make the first – or some other rate. IE I am suggesting (as is implied in your answer for one case) that we can expect the result of the second FTA to vary depending on the outcome of the first FTA.

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