# When a missile is fired from a ship,

Question:

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:

1. (1) $\frac{1}{8}$

2. (2) $\frac{1}{27}$

3. (3) $\frac{3}{4}$

4. (4) $\frac{3}{8}$

Correct Option: 1

Solution:

Probability of not getting intercepted $=\frac{2}{3}$

Probability of missile hitting target $=\frac{3}{4}$

$\therefore$ Probability that all 3 hit the target $=\left(\frac{2}{3} \times \frac{3}{4}\right)^{3}=\frac{1}{8}$