Find the minimum number of people in a room so that the probability that at least two of them have the same birthday is greater than 1/2.
2007-03-27 02:39:51 · 2 answers · asked by Life sucks . but u gonna love it 2 in Science & Mathematics ➔ Mathematics
23.
You should look at it as, "what are the probabilities that nobody in the room has the same birthday".
Odds of two people having different birthdays:
(365/365) * (364/365) = 99.7%
Odds of three people having different birthdays:
(365/365) * (364/365) * (363/365) = 99.2%
....
Odds of twenty-three people having different birthdays:
(365/365) * (364/365) *....* (342/365) = 49.3%
So in a room of twenty-three people, the odds that they all have distinct birthdays is less than 50%. Therefore, the odds that at least two of them share a birthday is greater than 50%.
2007-03-27 02:44:43 · answer #1 · answered by Chris D 2 · 2⤊ 0⤋
23... u get 253 different combinations... and 253 is more than half of 365
2007-03-27 02:54:10 · answer #2 · answered by kirlia7755 3 · 0⤊ 0⤋