Boys and Girls

Discrete Mathematics Level 4

Consider a family of \(n\) children. Define the events \(A\) and \(B\) as follows.
\(A\) is the event that the family has both boys and girls.
\(B\) is the event that he family has at most 1 girl.
Find the value of \(n\) such that events \(A\) and \(B\) are independent.

Assumptions and Clarifications

  • Probability that a randomly selected child is a boy or girl is same.
  • Two events are independent if occurrence of one does not affect the probability of the other.

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