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Birthday problem․ In probability theory‚ the birthday problem or birthday paradox concerns the probability that‚ in a set of n randomly chosen people‚ some pair of them will have the same birthday․ In

By Booze

Birthday problem․ In probability theory‚ the birthday problem or birthday paradox concerns the probability that‚ in a set of n randomly chosen people‚ some pair of them will have the same birthday․ In a group of 23 people‚ the probability of a shared birthday exceeds 50％‚ while a group of 70 has a 99․9％ chance of a shared birthday․ （By the pigeonhole principle‚ the probability reaches 100％ when the number of people reaches 367‚ since there are only 366 possible birthdays‚ including February 29․） These conclusions are based on the assumption that each day of the year is equally probable for a birthday․ Actual birth records show that different numbers of people are born on different days․ In this case‚ it can be shown that the number of people required to reach the 50％ threshold is 23 or fewer․［1］ The birthday problem is a veridical paradox˸ a proposition that at first appears counterintuitive‚ but is in fact true․ While it may seem surprising that only 23 individuals are required to rea