"We're thinking about children – with the assumption that babies are boys with probability 0.51, girls with probability 0.49, and births are independent.
You're a researcher interested in large families: as part of your latest project, you've decided to interview 50 families in which there are exactly eight children.
What's the probability that, in at least one of the 50 families, the children will all be of the same gender?"
I can't figure this one out.. If someone could at least help me with the correct formula, that would be awesome.
Best Answer
The probability that in any one family all of the eight children are of the same gender is $$p=0.51^8+0.49^8$$ The probability that, in at least one of the 50 families, the children will all be of the same gender is then $$q=1-(1-p)^{50}$$ (by complementarity.)