9/1/2014 Suppose there’s a 53% likelihood that a child born is Male. If a family has 6 children, what is the probability that at least 1 shall be a boy?

Scroll down for the solution.

9/1/2014 Solution. P(B) = 0.53

P(at least 1 boy amongst 6 children)
= 1 – P(no boy at all amongst the 6 children)
= 1 – P(B', B', B', B', B')
= 1 – P(B')⁶, assuming independence

= 1 – 0.47⁶

= 98.92%