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If 25 people are randomly selected, what is the probability that no 2 of them have the same borthday

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Assuming that there are 365 possible birthdays (excluding leap years), the probability that no 2 people have the same birthday can be calculated as follows:

The first person can have any birthday, so the probability is 1.

The second person must have a different birthday than the first person. The probability of this is 364/365, since there are 364 possible birthdays that the second person could have, out of 365 total possible birthdays.

The third person must have a different birthday than the first two people. The probability of this is 363/365, since there are 363 possible birthdays that the third person could have, out of 365 total possible birthdays.

Continuing this process, the probability that the 25th person has a different birthday than the first 24 people is:

(365/365) * (364/365) * (363/365) * ... * (342/365)

Multiplying these probabilities together, we get:

(365/365) * (364/365) * (363/365) * ... * (342/365) ≈ 0.4313

Therefore, the probability that no 2 people have the same birthday among a group of 25 people is approximately 0.4313, or 43.13%.

User Dmytro Vasin
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