Five People
HELP! What is the probability that in a group of five people, at least two share the same birthday...?
What is the probability that in a group of five people, at least two share the same birthday, assuming each birth date is equally likely (1/365). Ignore leap years.
P[at least 2 share birthday] = 1 - P[nonne share birthday]
for none to share birthday, the 1st person can be born on any day
and all others must be born on different days, so
P[none share birthday]
= 1*[364/365][363/365][362/365][361/365]
= 0.9729
so P[at least two share birthday] = 1 - 0.9729
ans: 0.0271 or 2.71%
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