Question

Tommy the Dunker's performance on the basketball court is influenced by his state of mind: If he scores, he is twice as likely to score on the next shot as he is to miss, whereas if he misses a shot, he is six times as likely to miss the next shot as he is to score.

Required:
a. If Tommy has missed a shot, what is the probability that he will score two shots later?
b. In the long term, what percentage of shots are successful?

Answer 1

Explanation:

Probability of of winning next shot if he scores= 0.5

Probability of missing next shot if he misses = 1/6

a) Probability of scoring 2 shots later if he missed = (1-1/6)^2

=(5/6)^2

=25/36

b) % of successful shots= (1/2+5/6×(1/100))%

=4/3×1/100

=0.013%