Probability of the 10th child as boy


#1

In the village where they stop having child after a boy is born but continue till they don’t, I agree that with no condition the probability of the child being boy is 50% and the overall ratio would be 1:1.

However, I still feel that given someone already has 9 girl child, probability of the 10th child as boy will not be 50%

Should not the Bayes formula apply here?


#2

Hi Kamal,

I feel that Bayes can be applied when there is a relation between the two process. Since, the event of 9 girl child and the 10th child are natural events which are independent of each other, the probability of the 10th child child being a boy is 50%.

Even if we try to apply Bayes formula and say that,
Event A = 9 girl children
Event B = 10th boy child
P(A|B) = 0.5 ^ 9
P(A) = 0.5 ^ 9
P(B|A) = 0.5
All of this because A and B are independent natural events.
Hence,
P(B) = P(B|A).P(A)/P(A|B) = 0.5

Thanks,


#3

Actually now I got it. The answer to my question is 50%, the probability of a child being girl does not change by the circumstances.

But yes, the ratio of boys to girls will change.
As illustrated by Douglas in this article, the ratio will be 1:1 only if the village has infinite families. For finite families the girls will be greater in ratio.