# compute the probability that at least 2 have the same birthday? [duplicate]

In a party of 5 persons compute the probability that at least 2 have the same birthday(month/day),assume a 365-day year.

• want to find the probability that at least 2 have the same birthday? – Liju May 11 '14 at 18:56
• Find the probability that none of them have same birthday and subtract it from 1 – avz2611 May 11 '14 at 19:06

• Choose $5$ unique birthdays: $\displaystyle\binom{365}{5}$
• Multiply by the number of permutations for $5$ people: $\displaystyle\binom{365}{5}5!$
• Divide by the total number of birthday-combinations for $5$ people: $\displaystyle\frac{\binom{365}{5}5!}{365^5}$
2. Calculate the probability of the opposite event, where at least $2$ birthdays are not unique:
• $\displaystyle1-\displaystyle\frac{\binom{365}{5}5!}{365^5}=2.7$%
Finally, as a little exercise, find the minimum number of people for which the probability that at least $2$ have the same birthday is more than $50$% (and realize that it's less than what you'd expect).