When a missile is fired from a ship, the probability that it is i…

MCQ

When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is

A
$\frac{1}{27}$
B
$\frac{3}{4}$
✓
$\frac{1}{8}$
D
$\frac{3}{8}$

✓

Answer

Correct option: C.

$\frac{1}{8}$

c
Required probability $=\left(\frac{2}{3} \times \frac{3}{4}\right)^{3}=\frac{1}{8}$

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