Imagine your friend has two children, and they specifically mention to you that one of them is a boy. What is the likelihood that the other child is also a boy?

Question

Anonymous · Accepted Answer

The gender of a child is an independent variable and is not dependent on the
gender of the other child. P(G, G) = P(B, B) = 0.25. P(B, G) = P(G, B) = 0.25
where B stands for a Boy and G stands for a Girl. If we know at least one of the
children is a boy, then we have three possible cases and out of them there is
only one case where both kids are boys. So, the probability is 1/3.

Anonymous · Answer

1/3

Apply the “at least one boy” condition"
The condition removes GG, leaving:

* BB

* BG

* GB

These are equally likely given the condition.

Find the probability the other child is also a boy
In this filtered list, only BB has both boys:

P(both boys|at least one boy)=1/3

Anonymous · Answer

The possible cases are boy boy, boy girl, girl girl, girl boy. Given one of the
kids is boy, there are 3 cases. There is only one case that another kid is a boy
so the probability is 1/3

Imagine your friend has two children, and they specifically mention to you that one of them is a boy. What is the likelihood that the other child is also a boy?

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