GATE CS 2026 Set 2 Q.3: Quantitative Aptitude

A day can only be cloudy or sunny. The probability of a day being cloudy is $0.5$ , independent of the condition on other days. What is the probability that in any given four days, there will be three cloudy days and one sunny day?

$1/4$

$3/4$

$2/3$

$3/8$

Official answer and solution

Official answer: A
From: Official GATE 2026 answer key

Solution

Apply the binomial probability distribution for $n=4$ independent trials with success probability $p=0.5$ .

Let $X$ be the number of cloudy days out of $n = 4$ independent days. Since each day is cloudy with probability $p = 0.5$ and sunny with probability $1 - p = 0.5$ , we have:

P(X = 3) = \binom{4}{3} (0.5)^3 (0.5)^1 = 4 \times \frac{1}{16} = \frac{1}{4}

Final answer

Option (A)

Common trap

Forgetting to multiply by $\binom{4}{3} = 4$ for the four possible positions of the sunny day.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 3 of 65
Section: General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source