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 it to play, a 30% chance that he will be somewhat it 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 it, 60% if he is somewhat it, 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 it to play in the game?