JEE PYQ: Probability Question 10
Question 10 - 2021 (25 Feb Shift 1)
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) $\frac{1}{8}$
(2) $\frac{1}{27}$
(3) $\frac{3}{4}$
(4) $\frac{3}{8}$
Show Answer
Answer: (1)
Solution
$P(\text{hit}) = P(\text{not intercepted}) \times P(\text{hit}|\text{not intercepted}) = \frac{2}{3} \times \frac{3}{4} = \frac{1}{2}$. $P(\text{all 3 hit}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8}$.
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