Question

The probability that A hits a target it 1/3 and the probability that B hits it is 2/5. If each one of A and B hits the target, find the probability that

(i) A hits the target

(ii) exactly one of them hits the target?

Answer 1

Given, P(A)=1/3 and P(B)=2/5
(i) A hits the target
Solution:
Since A and B both hit the target, here A can hit the target if B fails to hit
So A hits the target= P(A)(1-P(B)
=1/3*(1-2/5)
=1/3* 3/5
=1/5

(ii)Exactly one of them hits the target
Solution:
It can be done when one person hit the target others doesnot
So probability
=A hit B doesn't or B hit A doesn't
=P(A)(1-P(B)+P(B)(1-P(B))
=$$\begin{gathered} \frac{1}{3}(1-\frac{2}{5})+\frac{2}{5}(1-\frac{1}{3}) \\ =\frac{1}{3}\times \frac{3}{5}+\frac{2}{5}\times \frac{2}{3} \\ =\frac{1}{5}+\frac{4}{15} \\ =\frac{7}{15} \end{gathered}$$