When a missile is fired from a ship, the

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. $\frac{1}{27}$

  2. $\frac{3}{4}$

  3. $\frac{1}{8}$

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


Correct Option: , 3

Solution:

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

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