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 $0.x1$. Find $x$.

Answer 1

Given,The probability of an archer to hit the target when it is wind,$P\left(H/W\right)=0.4$

The probability of an archer to hit the target when it is not windy,$P\left(H/\overline{W}\right)=0.7$

The probability of gust of wind,$P\left(W\right)=0.3$

The probability that gust of wind doesn't exist,$P\left(\overline{W}\right)=1-P\left(W\right)=1-0.3=0.7$

$\therefore Theproabilitythatarcherwillhittargetonfirstshot,P\left(H\right)=P\left(H/W\right)\times P\left(W\right)+P\left(H/\overline{W}\right)\times P\left(\overline{W}\right)$

$=0.4\times 0.3+0.7\times 0.7=0.12+0.49=0.61$

$\therefore x=6$