re: Cashier at store told me one guy has spent $4000 on Powerball

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Recently my sister-in-law found out she was having twins, and her husband, an engineer, said, "there is a 2/3 chance of having a boy because there are three scenarios." I tried to explain that it's actually 3/4 (assuming 50/50 for each child), and he still looked unconvinced.

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Identical boys
Identical girls
Fraternal Boys
Fraternal Girls
Fraternal girl/boy
Identical boy/girl

4/6 = 2/3

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In other words, even quantitatively inclined individuals have trouble with the logic of probability.

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That is understandable when you consider how many people, even those with PhDs in mathematics, were stumped by the original Monty Hall problem.

Probability is difficult because it often goes against intuition and sometimes even against logic.

The twin deal is a perfect example. Logically you would deduce that there are 3 scenarios - BB, boy and girl, or GG. However, mathematically there are 4 scenarios because you can create an order for the twins. BG and GB are not the same with regard to probability as they are two distinct outcomes.

I think it is often easier in that situation to explain it using BB or GG as your basis - meaning it may be easier to explain that there is a 25% chance of having two girls, so obviously there is a 75% chance of having at least one boy.