Detective Cluespot was putting together the suspect's profile. It was known that the suspect had two children and that one of them was a boy. What is the probability that the suspect's other child is also a boy?

It's not what you may think!

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*"Here are four questions. They sound very similar. But be careful. They are not.
1. Mrs Smith has two children. The eldest one is a boy. What’s the chance that both are boys?
2. Mrs Jones has two children. At least one is a boy. What’s the chance that both are boys?
3. Mrs Robinson has two children. At least one is a boy born on a Monday. What’s the chance that both are boys?
4. Mrs Taylor has two children. At least one is a boy called Oscar. What’s the chance that both are boys?
(Assume Mrs Smith, Jones, Robinson and Taylor are each chosen randomly from the population of families with exactly two children. The phrase ‘at least one is a boy’ is understood in the literal sense, i.e. in this case either one child is a boy, or both children are boys.)
You might think that the boy’s day of birth, or indeed his name, are irrelevant. If you do, you are wrong. The answers are all different.
This was Alex Bellos's Monday puzzle in the Guardian newspaper. The answers can be found here: The Guardian."*

*Extension,
Tuesday, November 19, 2019*

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