Question

When a missile is fired from a ship, the probability that it is intercepted is 1/3 and 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, then the probability that all three hit the target, is :

• A. 1/27
• B. 1/8
• C. 3/8
• D. 3/4

Hint:

For independent events, the probability of the intersection is the product of the individual probabilities: $P(A \cap B \cap C) = P(A)P(B)P(C)$.

Answer 1

The Correct Option is B

Step 1: $P(\text{Not Intercepted}) = 1 - 1/3 = 2/3$.
Step 2: $P(\text{Hit} | \text{Not Intercepted}) = 3/4$.
Step 3: $P(\text{Hit}) = P(\text{Not Intercepted}) \times P(\text{Hit} | \text{Not Intercepted}) = \frac{2}{3} \times \frac{3}{4} = 1/2$.
Step 4: For 3 independent missiles: $P(\text{All Hit}) = (1/2)^3 = 1/8$.