The probability of a boy or a girl being born is 1/2. For a family having only three children, what is the probability of having two girls and one boy? A. 3/8 B. 1/8 C. 1/4 D. 1/2

GATE 2024 · General Aptitude · Probability · medium

Answer: P(exactly 2 girls and 1 boy in 3 children) = 3/8.

1. Identify the favorable sequences: n = 3, k = 2 girls. C(3, 2) = 3. Sequences: GGB, GBG, BGG — three arrangements.
2. Compute probability of each arrangement: P(GGB) = (1/2)*(1/2)*(1/2) = 1/8. Same for GBG and BGG since p = 1-p = 1/2.
3. Apply binomial probability formula: P(X = 2) = C(3,2) * (1/2)^2 * (1/2)^1 = 3 * (1/4) * (1/2) = 3 * 1/8 = 3/8.