Let A be the event that aeroplane-I hit the target correctly and B be the event that aeroplane-II hit the target correctly. ⇒P(A)=0.3 and P(B)=0.2 ∴P(A′)=1−P(A)=1−0.3=0.7 where A′ , first misses the target P(B′)=1−P(B)=1−0.2=0.8 B′ , second misses the target. Let X be the event that target is hit by plane-II ∴P(X)=P(A′)P(B)+P(A′)P(B′)P(A′)P(B)+P(A′)P(B′)P(A′)P(B′)P(A′)P(B)+..... =0.7×0.2+0.7×0.8×0.7×0.2+0.7×0.8×0.7×0.8×0.7×0.2+.... =0.14[1+(0.56)+(0.56)2+....] =0.14[
1
1−0.56
]=0.14×
1
0.44
=0.32 [∵1+0.56+(0.56)2+.... forms an infinite GP whose sum =
a
1−r
where a is first term and r is common ratio] ∴P(X)=0.32