In: Statistics and Probability
Kay has an 80% probability of making a free-throw in basketball, and each free-throw is independent. Kay gets to take 2 free-throws, and must make both to win the game. What is the probability that Kay's team will win the game?
1. 64%
2. 80%
3. 88%
4. 160% (so 100%)
Define the events
A=Kay makes the first throw
B=Kay makes the second throw
Then P(Kay's team will win the game)=P(Kay makes both)=P(A and B)=P(A)P(B) as different throws are independent.
Now P(A)=P(B)=.80, so that
P(Kay's team will win the game)=P(Kay makes both)=P(A and B)=P(A)P(B)=.8*.8=.64
Hence the required chance is 64%.
Thus the correct option is (1).