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Question

In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is
  1. 0.667

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Solution

The correct option is A 0.667
Let E1=One children family
E2=Two children family
A = Picking a child
By Baye's theorem

P(E2/A)=P(E2)P(A/E2)P(E1)P(A/E1)+P(E2).P(A/E2)

=12.x12.x2+12.x=23=0.667

Method II:
Let there are 50 families of each type. So 50 children have no siblings and 100 children have siblings.

So, required probability =100C1150C1=100150=23

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