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What if they are twins? The explanation does not cover that and it sure changes the probabilities.

If we're going to bring reality into this, I think we have to take into account the fact that only very weird people tell you that "at least one child is a boy born on a Tuesday" and we have to consider the possibility that they are lying in order to test your knowledge of probability.

And if we're really going to bring reality into this, then we'll need to consider the ages of the children, because of the at-birth sex ratio (105 newborn boys for every 100 newborn girls[0]) and differing mortality rates for each sex.

[0]http://en.wikipedia.org/wiki/Human_sex_ratio

I think it's probably good to be precise in this case. It should state that "at least one child is a boy born on a Tuesday, but one is older than the other by at least a day".

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