Question

The probability that an archer hits the target when it is windy is 0.4; when it is not windy, her probability of hitting the target is 0.7. On any shot, the probability of a gust of wind is 0.3. The probability that she hits the target on first shot is 0.x10.x1. Find xx.

Answer 1

x = 6

Explanation:

The probability that this archer hits her first shot is given by t the probability of being windy and that she hits the shot added to the probability of not being windy and that she hits the shot:

`P(H_(first)) = P(H_w)*P(W)+P(H_(nw))*(1-P(W))\\P(H_(first))=0.4*0.3+0.7*(1-0.3)\\P(H_(first))=0.12+0.49 = 0.61`

If the probability that she hits the target on her first shot is 0.x1, the value of x is:

`P(H_(first))=0.61=0.x1\\x=6`