Birth season paradox

Probability Level 1

The birthday paradox is a surprising result of probability. Suppose you randomly chose 23 people and put them in a room. Then there would be a good chance (\big(greater than 12)\frac{1}{2}\big) that two of those people share a birthday (even though there are 365 days in the year).

What about birth seasons (spring, summer, fall, winter)? Suppose you randomly chose 3 people and put them in a room. Then is it true that there would be a greater than 12\frac{1}{2} chance that two of them share a birth season?


Note: Birth seasons do not all have the exact same likelihood. However, their likelihoods are close enough that you can assume they are equal for this problem.

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