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GATE CSE 2026 Session 2 Q3: Probability of three cloudy days in four

Question

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?

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Answer: A (official GATE 2026 final answer key)

Concept used: Binomial probability with n=4n = 4, p=0.5p = 0.5.

First step: Count the ways to pick the one sunny day: (41)\binom{4}{1}, each sequence having probability (1/2)4(1/2)^4.

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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