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 :

Solution

Maths sir · 3 steps

First find the chance one missile hits, then cube it, because the three missiles are independent.

1. One missile hits. A missile can hit only if it is not intercepted. So P(hit) = P(not intercepted) × P(hit | not intercepted).

   P(hit) = (1 - 1/3) × 3/4 = 2/3 × 3/4 = 1/2

2. Three independent missiles. The missiles are fired independently, so the probability that all three hit is the product of the three single-missile probabilities: (1/2)³ = 1/8.
3. So. The probability that all three missiles hit the target is 1/8, option (d).

The idea to keep. A conditional probability is not the full probability. Multiply it by the chance of its condition, P(A ∩ B) = P(B) P(A | B), and only then combine independent trials.

Answer from the NTA final answer key. Solution by PrepWiser.