Other Child's Gender

Answer

More Advanced Lesson Starters

More Mathematics Lesson Starters

Extension,

Tuesday, November 19, 2019

"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."

Grange Academy Newsletter, Mathematics Department

Saturday, April 26, 2025

"Imagine that the government naively try to get more girls into Mathematics and Science careers by introducing an extreme new law to control the population: from now on, every woman who gives birth to a boy can have no more children.

So under this new regime, you could see families with at most one son but some families would have all girls or four children where three are daughters and one is a son or in extremely large families you could imagine ten children (nine daughters and one son).

Seems like this could work, eh? Surely the population will have more girls.

Not really.

Think about all the mothers with only one child. Half of their children will be boys, half girls.

Those mothers who have girls and continue to have a second child will either have a boy (and stop having kids) or a girl. But the distribution is still the same.

Half of these can continue to have a third child and again this will generate an equal split of boys and girls. Every round produces equal ratios of boys and girls so it doesn’t matter how many rounds or the sizes of the families, the sex ratio will be unaffected!"

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