NDA 1 2024 Maths, question 115

Topic: Probability

Passage · Q115 to Q116

An unbiased coin is tossed $n$ times. The probability of getting at least one tail is $p$ and the probability of at least two tails is $q$ and $p-q=\frac{5}{32}$ .

Q115

What is the value of $n$ ?

(a) $4$
(b) $5$ Correct answer
(c) $6$
(d) $7$

Solution.

Answer: (b) $5$

The difference between the probabilities of at least one and at least two tails is the probability of exactly one tail: n/2ⁿ = 5/32.
This holds for n = 5.
For integer n ≥ 2, n/2ⁿ strictly decreases, which confirms uniqueness among the choices.