Q56 / 120 · JEE Main 2007 · Mathematics

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

  • A
    $0.06$
  • B
    $0.14$
  • C
    $0.2$
  • Correct answer
    D
    None of these

Solution

The desired probability $\begin{aligned} & =0.7 \times 0.2+(0.7)(0.8)(0.7)(0.2)+(0.7)(0.8)(0.7)(0.8)(0.7)(0.2)+\ldots . \\ & =0.14\left[1+(0.56)+(0.56)^2+\ldots\right] \\ & =0.14\left[\frac{1}{1-0.56}\right]=\frac{0.14}{0.44}=\frac{7}{22}. \end{aligned}$

Hence, the correct answer is option: 'D'.

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