Two aeroplanes I and II bomb a target in succession. The probabilities of I and II 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 (1) 0.06 (2) 0.14 (3) 0.2 (3) 0.7

Options

A. 0.06
B. 0.14
C. 0.32
D. 0.7

Answer

C

Explanation

Let A and B are the lst and llnd aeroplane hit the target respectively and their corresponding probabilities are
`P(A)=0.3" and "P(B)=0.2`
`impliesP(barA)=0.7" and "P(barB)=0.8`
`:.` Required probability
`=P(barA)P(B)+P(barA)P(barB)P(barA)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))=0.32`