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Birthday at the cinema

Birthday at the cinema

In a movie theater with capacity for 400 people, the latest film by a well-known Spanish director is released. Knowing that the room occupancy is 95%,

What is the probability that two people turn years the same day?

Solution

If the capacity of the room is 400 people and it is 95% complete, we have 380 people in the room. If we assume the worst possible scenario in which we have a person who turns years for each of the days of the year, we have 366 people turn years on different dates (including leap years), but the person who makes the number 367 must obligatorily meet years on the same day as any of the first 366, so the probability is 1.

Surely two people will turn years the same day.