Skip to content
GATETECH
Official PYQ · 2026Set 2 · Q3MCQ1 mark

GATE CS 2026 Set 2 Q3 — General Aptitude

Explain with AI

A day can only be cloudy or sunny. The probability of a day being cloudy is 0.50.5, 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?

Choose one option
View worked solution

Answer: A

This problem can be modeled using the Binomial Distribution, where each day is an independent trial with two possible outcomes: cloudy (success) or sunny (failure).

Let:

  • n=4n = 4 be the total number of days.
  • k=3k = 3 be the desired number of cloudy days.
  • p=0.5p = 0.5 be the probability of a day being cloudy.
  • q=1−p=0.5q = 1 - p = 0.5 be the probability of a day being sunny.

The probability of getting exactly kk successes in nn independent trials is given by the binomial formula:

P(X=k)=(nk)pkqn−kP(X = k) = \binom{n}{k} p^k q^{n-k}

Substituting the given values into the formula:

P(X=3)=(43)(0.5)3(0.5)4−3P(X = 3) = \binom{4}{3} (0.5)^3 (0.5)^{4-3}P(X=3)=4×(0.5)4=4×116=14P(X = 3) = 4 \times (0.5)^4 = 4 \times \frac{1}{16} = \frac{1}{4}

Thus, the probability that there will be three cloudy days and one sunny day in any given four days is 14\frac{1}{4}.

Therefore, the correct option is A.

Free practice · Your answers on this page are not saved.

Published
Report a correction
Keep exploringMore General Aptitude questions