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


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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