A basketball player who shoots 80% from the free-throw line goes to the charity stripe with just 1.7 seconds remaining in a basketball game.
He has two shots, and his team is trailing by two points.

What is the probability that he will make only one of the two, and why?

(Assume that he is trying, of course, for his team to win the game.)

(In reply to how to win by Roger)

Whoa, buddy...that all may sound good, but nothing that would even happen in a game..

First, the ultimate strategy in this case would invariably be to try to make both foul shots and put the game into overtime. So, he will always try to make the first shot.

Then, if he makes the first shot, the strategy is unchanged. He is always going to try to make the second shot if he had made the first.

If he misses the first shot, then making the second shot will do no good. They'll still be down by a point, and the other team gets the ball with only 1.7 seconds left.

The only viable choice here is to intentionally miss the second shot, hoping for a teammate to get the rebound and put the ball back up for two points and a tie.

Also, do you know how hard it is to bounce a ball off the backboard, from the free throw line (15 feet away), and make it out to the three-point line (20-24 feet out)? Add that to the fact that he has only one teammate back there, with a man on him, and his other three teammates are between him and the basket -- they're not going to try it. Not that it changes the answer to this question at all, except that he's probably more likely to accidentally make the shot if he's trying to put it out to the 3-point line than dropping it inside the key.

Even still, 2 foul shots by an 80% shooter in a two-point game is far from hopeless, so while miracles do indeed happen every day, one will likely not even be necessary for this game.

Posted by DJ on 2003-08-17 14:50:41