The Birthday Problem and Some Generalizations

problem

same day

within one day

number of days in the year

365

desired probability

0.5

reset

guess
show answer

If there are

365

days in a year, how many people are needed in order for the probability that at least two people share a birthday to exceed

0.5

? Enter a guess to the left.

The birthday problem asks, "How many randomly selected people must there be in a room in order for the probability that two people share a birthday to exceed 0.5?" and has the well-known answer 23. The following generalizations are illustrated here, along with answers:

1. The probability of 0.5 can be replaced by any value from 0.01 to 0.99, in increments of 0.01.

2. The number of days in a year can be any value from 2 through 5000, for the convenience of extraterrestrials.

3. The question "How many randomly selected people must there be in a room in order for the probability that two people share a birthday or have birthdays on consecutive days to exceed 0.5?" is investigated.

Any combination of these generalizations can be used simultaneously.