Correct : a

The correct answer is Option A — 1/4.
This is a classic Binomial probability problem. Each day independently has probability p = 0.5 of being cloudy and q = 0.5 of being sunny. We need exactly 3 cloudy days out of 4, which follows the binomial formula:
P(X = k) = C(n, k) × p^k × q^(n−k)
Here n = 4, k = 3, p = 0.5, q = 0.5:
P(X = 3) = C(4, 3) × (0.5)³ × (0.5)¹ = 4 × (1/8) × (1/2) = 4/16 = 1/4.
C(4, 3) = 4 accounts for the 4 different ways to choose which 3 of the 4 days are cloudy (CCCS, CCSC, CSCC, SCCC). Each such arrangement has probability (0.5)³ × (0.5)¹ = 1/16. Multiplying gives 4/16 = 1/4.
Why not Option D (3/8)? A common mistake is computing C(4,3) × (0.5)³ = 4/8 = 3/8, forgetting to multiply by (0.5)¹ for the one sunny day. Since the sunny day also has probability 0.5, it must be included in the product — giving (0.5)⁴ total, not (0.5)³.
Why not Option A being confused with 1/4 by intuition? One might guess 1/4 simply because 1 out of 4 days is sunny, but the actual derivation confirms the answer rigorously through the binomial formula.