Suppose you play a carnival game that requires you to toss a ball to hit a target. The probability that you will hit the target on each play is .2 and is independent from one try to the next. You win a prize if you hit the target by the third try.
a. What is the probability that you hit the target on the first try?
b. What is the probability that you miss the target on the first try but hit it on the second try?
c. What is the probability that you miss the target on the first and second tries but hit it on the third try?
d. What is the probability that you win a prize?