Two aeroplanes [ I] and [ I] I[ bomb a target in succession.

Question

Two aeroplanes $${\rm I}$$ and $${\rm I}$$ ${\rm I}$$ bomb a target in succession. The probabilities of $${\rm I}$and${\rm I}$$ ${\rm I}$$ scoring a hit correctly are $0.3$ and $0.2,$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is :

Accepted Answer

The desired probability

= (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 $$\left( {{1 \over {1 - 0.56}}} \right) = {{0.14} \over {0.44}} = {7 \over {22}}$$ = 0.32

Solutions · 1