Q80 / 150 · MHT CET 2008 · Mathematics

A parents has two children. If one of them is boy, then the probability that other is, also a boy, is

  • A
    $1 / 2$
  • B
    $1 / 4$
  • Correct answer
    C
    $1 / 3$
  • D
    None of these

Solution

Total cases are $B B, B G, G B, G G=4$ Favourable cases are $B B, B G, G B=3$ Let $P(A)=$ Probability of a boy in two children $$ =\frac{3}{4} $$ The probability that the second child is also a boy is $P(A \cap B)=\frac{1}{4}$ We have to find $P(B / A)=\frac{P(A \cap B)}{P(A)}=\frac{1 / 4}{3 / 4}=\frac{1}{3}$

Hence, the correct answer is option: 'C'.

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