JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Probability

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 probability that all three hit the target, is :

Answer: (D)

Solution

For a single missile,

P (not intercepted) = 1 - \frac{1}{3} = \frac{2}{3}

. Given not intercepted,

P (hit) = \frac{3}{4}

. So

P (hit) = P (not intercepted) \times P (hit ∣ not intercepted) = \frac{2}{3} \times \frac{3}{4} = \frac{1}{2}

. For three independent missiles,

P (all three hit) = (\frac{1}{2})^{3} = \frac{1}{8}

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option