STATS QUESTION A basketball player has an 80% chance of making the first free-throw he shoots.

Question

A basketball player has an 80% chance of making the first free-throw he shoots. If he makes the first free-throw shot, then he has a 90% chance of making the second free-throw he shoots. If he misses the first free-throw shot, then he only has a 70% chance of making the second free-throw he shoots. Suppose this player has been awarded two free-throw shots. Find the probability that he makes at least one of the two shots.

Answer 1

probability makes at least 1 or 2 = probability he make 1 or 2 = 1 - probability he make none

probability miss first = 0.2 probability miss 2nd after missing first = 0.3. probability miss both = 0.2 * 0.3 = 0.06

probability make at least 1 = 1 - 0.06 = 0.94