When a missile is fired from a ship, the probability that is intercepted is 1/3. The probability that the missile hits the target, given that it is not intercepted is 3/4. If three missiles are fired independently from the ship, the probability that all three hits the target, is

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$\frac{1}{8}$

$\frac{3}{4}$

$\frac{3}{8}$

$\frac{1}{12}$

answer is B.

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Detailed Solution

R : Missile is intercepted
$P (R) = \frac{1}{3}; P (\bar{R}) = \frac{2}{3}; P (\frac{H}{\bar{R}}) = \frac{3}{4}$
H: Missile hits the target
$\begin{array}{l} P (H) = P (H \cap R) + (H \cap \bar{R}) \\ = P (R) \cdot P (\frac{H}{R}) + P (\bar{R}) \cdot P (\frac{H}{\bar{R}}) \\ = \frac{1}{3} \cdot (0) + \frac{2}{3} \cdot \frac{3}{4} = \frac{1}{2} Hence P (HHH) = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8} \end{array}$

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