Steve has two kids and one of them is a boy. What is the probability

Question

Steve has two kids and one of them is a boy. What is the probability the other child is also a boy?

A) 1.00
B) 0.75
C) 0.50
D) 0.33
E) 0.25

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JerryAtDreamScore · Answer

Breaking Down the Info:

Gender is independent, so the probability is simply 50% (or 50.5% if we want to use world population as an estimate!)

Answer: C

Regor60 · Answer

Birth order is independent, but that is only the beginning of the solution.

One of the children is a boy, so the children could have been born:

BB BG GB

In only 1 of these is the "other" child also a boy.

Probability 1/3

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IanStewart · Answer

There are three perfectly legitimate answers to this question, depending on how we've come to learn that one of Steve's children is a boy:

• if we see Steve walking around a supermarket with a random one of his children, and that child is a boy, then the probability the other child is a boy is 1/2. The biological sex of the child in the supermarket has nothing to do with that of the child at home -- so if we just learn one specific child is a boy, the answer is 1/2

• if Steve's children are school age, and we learn one of them is enrolled at King Preparatory, an all-boys school, and we know Steve would always send a son to King Preparatory, then there are three equally probable scenarios where Steve could send a son to King Preparatory: he had a girl then a boy, a boy then a girl, or two boys. So then the answer is 1/3 (or the answer is 1/3 in any situation where we somehow learn Steve has at least one boy)

• if Steve just tells us "I have two children and one of them is a boy", then the probability the other child is a boy is presumably zero, because why wouldn't Steve just say "I have two children and both of them are boys"?

the above all assuming the probability a randomly born child is a boy is 1/2 and a girl is 1/2. I'd assume the answer is meant to be 1/3 here, and that we're meant to understand from the question that Steve has at least one son, but it's really not possible to guess from the wording what the question truly means.

Steve has two kids and one of them is a boy. What is the probability

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