Question: A crucial game of the Los Angeles Lakers basketball team depends on the health of their key player. According to his doctor's report, there is a 40% chance that he will be fully fit to play, a 30% chance that he will be somewhat fit to play, and a 30% chance that he will not be able to play at all. The coach has estimated the chances of winning at 80% if the player is fully fit, 60% if he is somewhat fit, and 40% if he is unable to play.
a. What is the probability that the Lakers will win the game?
b. You have just heard that the Lakers won the game. What is the probability that the key player had been fully fit to play in the game?