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The Brooklyn Nets are playing basketball against the Milwaukee Bucks. There are ten seconds left in the game, and the Bucks are ahead by one

The Brooklyn Nets are playing basketball against the Milwaukee Bucks. There are ten seconds left in the game, and the Bucks are ahead by one point, so the Nets need two points to win. The Nets send Kevin Durant to take a final shot. Three things could happen:

  • If Durant makes the shot, he will get two points.
  • If Durant misses the shot and does not get fouled, he will get zero points.
  • If Durant misses the shot and gets fouled, he will have the opportunity to shoot two free throws. Each free throw is worth 11 point if he makes it.

We make some estimates based on past games:

  • The probability of Durant making the first shot is50%.
  • The probability of Durant missing the shot and not getting fouled is 25%.
  • If Durant misses and gets fouled, the probability of making each free throw is 88% (and they are independent), so the probability of making both free throws is 88% x 88 % = 77.44, which we'll round to 77%.

What is the probability that Durant will score two points?

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