In: Statistics and Probability
If a family has six children, is it more likely they will have three boys and three girls, or four of one gender and two of the other? Assume each child is a boy or a girl with equal probability, independently of other children.
P(Three boys and three girls)
= 0.3125
P(Four of one gender and two of other)
= P(Four boys; 2 girls) + P(4 Girls; 2 Boys)
= 0.46875
Hence,
Four of one gender and two of the other is more likely.