Probability of gender in offspring
Name: neel k gupta
Date: Around 1995
The probability of a certain couple having a girl is 3/4, a boy, 1/4. What
is the probability of having 4 girls in a row given that a) they have at
least one girl b) they have at least 3 girls?
Pr[GGGG] = (0.75)^4
Pr[BBBB] = (0.25)^4
Pr[BGGG or GBGG or GGBG or GGGB] = 4*(0.25)*(0.75)^3
Now the division rule for conditional probability applies and denoting the
three numbers above by x, y, and z, we get
x/(1-y) or 81/255 for the first problem and
x/(x+z) or 81/117 for the second problem.
On the other hand, some couples are more prone to either male or female
offspring. If they already have three girls the probability of a fourth
might be much higher than you would expect!
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Update: June 2012