This is why I sometimes hate probability. The probabilities here strongly depend on how the family and boys are chosen.
If you took a list of families with exactly two children and threw out the ones that had no boys, then you’d find that of the remaining families, 1⁄3 have two boys.
If you took a list of boys who have exactly one sibling and asked how many of them had a brother, you’d get the answer 1⁄2.
The difference is whether the child is chosen at random. Even a minor change in the phrasing of the question can change the correct answer. Always be cautious with probability.
| oldest | youngest |
+--------|----------|
| boy... | boy..... | two boys
| boy... | girl.... | one boy
| girl.. | boy..... | one boy
| girl.. | girl.... | no boys
(And is it not weird, how two questions of the same, well, validity, give two different answers and perhaps—in a situation, where it matters—lead to different formulations?)
This is why I sometimes hate probability. The probabilities here strongly depend on how the family and boys are chosen.
If you took a list of families with exactly two children and threw out the ones that had no boys, then you’d find that of the remaining families, 1⁄3 have two boys.
If you took a list of boys who have exactly one sibling and asked how many of them had a brother, you’d get the answer 1⁄2.
The difference is whether the child is chosen at random. Even a minor change in the phrasing of the question can change the correct answer. Always be cautious with probability.
Why 1/3?
Families with exactly two children:
Thank you. I should have realised that.
(And is it not weird, how two questions of the same, well, validity, give two different answers and perhaps—in a situation, where it matters—lead to different formulations?)