The GATE Grind

GATE 2024 CY – Question 7

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

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?

  1. 3/8
  2. 1/8
  3. 1/4
  4. 1/2

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 3/8

Explanation

Each birth is a boy or a girl with probability $\tfrac12$, independently. For three children there are $2^3=8$ equally likely sequences.

**Favourable outcomes** (two girls and one boy): GGB, GBG, BGG, which is 3 outcomes.

$$P=\frac38 .$$

(Using the binomial formula: $\binom32\left(\tfrac12\right)^2\left(\tfrac12\right)=3\times\tfrac18=\tfrac38$.)

Answer **3/8** (A).