The estimated probability of a bowler getting a strike during a particular frame is 63%. if several simulations of the bowler bowling two frames were performed, in what percentage of the simulations would the bowler be most likely to get a strike in each of the two frames?
a. 81%
b. 38%
c. 18%
d. 61%

option b. 38%.

Explanation:

1) Getting strikes are independent events; this is, the probability of getting a strike is not affected on whether you got or not an strike in other chance.

2) The probability of occurrence of two independent events is calculating multiplying the probabilities of the two events:

P ( A and B) = P(A) × P (B)

3) Therefore, the probability of bowler to get a strike in two frames is the product of the probabilities to get a strike in each frame, which is:

P (strike on frame 1 and strike on frame 2) = P(strike on frame 1) × P (strike of frame 2):

63% × 63% = 0.63 × 0.63 = 0.3969 = 39.69%.

Therefore, a simulation most likely get 38% instead of 81%, or 18%, or 61%, that is why the answer is the option b. 38%.