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GATE 2026 CS (CS2) – Question 3

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

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. $\frac{1}{4}$
  2. $\frac{3}{4}$
  3. $\frac{2}{3}$
  4. $\frac{3}{8}$

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Show answer and explanation

Correct answer: (A) $\frac{1}{4}$

Explanation

The number of ways to choose exactly 3 cloudy days out of 4 days is $\binom{4}{3}=4$. Since each day is independently cloudy with probability $\frac{1}{2}$, each specific 4-day pattern has probability $\left(\frac{1}{2}\right)^4 = \frac{1}{16}$. Hence, the required probability is $\binom{4}{3}\frac{1}{16}=\frac{4}{16}=\frac{1}{4}$. Therefore, option (A) is correct.