NDA 1 2025 Maths, question 108

Topic: Probability

Passage · Q107 to Q108

Let $X$ be a random variable following binomial distribution with parameters $n = 6$ and $p = k$ . Further, $9P(X = 4) = P(X = 2)$ .

Q108

What is the value of $P(X = 3)$ ?

Solution.

Answer: (a) 135/1024

With $k = 1/4$ from question 107: $P(X = 3) = \binom{6}{3}\left(\frac{1}{4}\right)^{3}\left(\frac{3}{4}\right)^{3}$ .
$= 20 \times \frac{27}{4096} = \frac{540}{4096} = \frac{135}{1024}$ .

Trap: This uses $k = 1/4$ ; the degenerate values $k = 0$ or $1$ from question 107 would give 0, which is not an option.