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