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Question

# Two aeroplanes 1 and 2 bomb a target in succession.The probability of 1 and 2 scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only when 1st one misses the target.The probability that the target is hit by 2nd plane is?

A

0.40

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B

0.36

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C

0.32

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D

0.7

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Solution

## The correct option is C 0.32 For 2nd plane to hit the target following event will happen: Let P(A)= Probability that 1st plane hits the target: 0.3 P(B)= Probability that 2nd plane hits the target: -.2 P(E)=P(A)′P(B)+P(A)′P(B)′P(A)′P(B)+P(A)′P(B)′P(A)′P(B)′P(A)′P(B)................∞ This is an infinite GP with common ratio ′r′=P(A)′P(B)′ Sum=a1−r a=P(A)′P(B)=0.7×0.2=0.14 r=0.7×0.8=0.56 P(E)=0.141−0.56 P(E)=0.140.44 APPROXIMATELY=0.32

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