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GATE 2024 DA – 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

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Show answer and explanation

Correct answer: (A) 3/8

Explanation

There are $2^3 = 8$ equally likely sequences of three births. The ones with two girls and one boy are GGB, GBG and BGG, 3 in all, so the probability is $\frac{3}{8}$ (or $\binom{3}{2}\left(\frac{1}{2}\right)^3$).