NDA 2 2024 Maths, question 107

Topic: Probability

Q107

$A$ can hit a target $5$ times in $6$ shots, $B$ can hit $4$ times in $5$ shots and $C$ can hit $3$ times in $4$ shots. What is the probability that $A$ and $C$ may hit but $B$ may lose?

(a) $1/8$ Correct answer
(b) $1/6$
(c) $1/4$
(d) $1/3$

Solution.

Answer: (a) $1/8$

$P(A \text{ hits}) = \frac{5}{6}$ , $P(B \text{ misses}) = 1 - \frac{4}{5} = \frac{1}{5}$ , $P(C \text{ hits}) = \frac{3}{4}$ .
Multiply: $\frac{5}{6} \times \frac{1}{5} \times \frac{3}{4} = \frac{15}{120} = \frac{1}{8}$ .

Trap: Multiplying assumes the three shoot independently, which the question takes for granted.