Discussion
How many people must there be in a room before there is a 50% chance that two of them were born on the same day of the year ?
Answer: A
At least 23 people are needed for a better than 50% chance that two of them share a birthday, the birthday paradox. The probability that all of n people have different birthdays is \(\frac{365 \times 364 \times \cdots \times (365-n+1)}{365^{n}}\), which drops below 0.5 at n = 23.
The number 183 is about half of 365 and is the answer to a different question, how many people are needed for a 50% chance that one of them shares your own birthday. The numbers 366 and 730 relate to the pigeonhole principle, which guarantees a match but not at the 50% level.
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