probability 101

Years ago I shared a probability problem with a Quantitative Analysis professor who used it as an introduction to a statistics course on the first day of classes. Here it is.

“Two Boys Problem”:

A man and a woman each have two children. The man and his children are not related to the woman and her children. If the woman’s older child is male and the man has at least one son, is the probability that the woman has two sons equal to the probability that the man has two sons?

In his class of brilliant overachievers of roughly 50 people, all agreed that the probabilities between the man and woman were equal–except for one lone dissenter whose hand slowly raised.

The lone dissenter was correct. Here’s why.

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