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NDA 2017 Maths · Mathematics · Probability · medium

In a family of three children, the probability that there is at least one boy and at least one girl is (assuming equal chances for each)

Single correct option

In a family of three children, the probability that there is at least one boy and at least one girl is (assuming equal chances for each)
  1. A. 12\frac12
  2. B. 34\frac34
  3. C. 78\frac78
  4. D. 58\frac58
Show answer and solution

Answer: (B) 34\frac34

There are 23=82^3=8 equally likely outcomes. Only BBB and GGG fail the condition, so the probability is 1−28=341-\frac28=\frac34. The value 78\frac78 is the probability of at least one boy, which ignores the girl condition.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake