In a basketball game, one can attempt a 2 point score or a 3 point score. Suppose that 70% of the time, the team with the ball attempts a 2 point score. 30% of the time, the team attempts a 3 point score. Let there be a 45% chance that a 2 point score attempt succeeds and a 55% chance that it will fail. Suppose that for the 3 point score attempt, it will succeed 35% of the time and fail 65% of the time.
Fill in the values to the following tree diagram. (use 2 to 3 digits).
.AA = .70 .CC = .45 .GGGG =
.DD = .55 .HHHH =
.BB = .30 .EE = .35 .IIII =
.FF = .65 .JJJJ =
a. What is the probability that there will be a 2 point score?
P(2 point score) =
b. What is the probability that there will be a 3 point score?
P(3 point score) =
c. What is the probability that there will be no score after an attempt?
P(no score) =
d. Given that there is there is no score after an attempt, what is the probability that the attempt was a failed 3 point score attempt?
P(3 point score failed attempt | no score) =