I have two children. At least one of them is a boy. What is the probability that the other one is a boy as well?
There are four orders the children could have been born.
BB
BG
GB
GG
Of those, three cases have at least one boy in them. Only one of those three has a boy with a brother. So, the answer is 1/3.
Answer to "John's Brother": 1/4A man has two children. One of them is a boy named John. What is the probability that John has a younger brother?
The pairs of children are the same:
BB
BG
GB
GG
If one of the children is a boy, we have the same situation as before:
BB
BG
GB
If one of the boys is named John, there are four possible cases now. Note the first two both come from the original BB possibility.
JB
BJ
JG
GJ
The probability that “John” has a younger brother is 1 in 4.
The pairs of children are the same:
BB
BG
GB
GG
If one of the children is a boy, we have the same situation as before:
BB
BG
GB
If one of the boys is named John, there are four possible cases now. Note the first two both come from the original BB possibility.
JB
BJ
JG
GJ
The probability that “John” has a younger brother is 1 in 4.
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