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The answer depends on how refined the theory is. The simplest theory is that birthdays are distributed evenly through the year across the world. If that were the case, the answer is 1/2.

However, anyone who has spent even a short time studying the subject will know that birthdays are not evenly distributed. The month to month variations, plus differences between countries need to be taken into account before a half-way decent theoretical model can be constructed.

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Q: What is the theoretical probability of randomly choosing a person at the business who has a birthday in the first half of the year?
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