Question

Consider n people who are attending a party. We assume that every person has an equal probability of being born on any day during the year, independently of everyone else, and ignore the additional complication presented by leap years (i.E., nobody is born on february 29). What is the probability that each person has a distinct birthday?

Answer 1

Given:

Consider n people who are attending a party. We assume that every person has an equal probability of being born on any day during the year, independently of everyone else, and ignore the additional complication presented by leap years (i.E., nobody is born on february 29).

To find:

The probability that each person has a distinct birthday

Solution:

Probability of event happening = Number of ways it can happen  / Number of possible events .

prob(2 people have different birthdays)

= 365/365  × 364 /365  ≈ 0.997

Similarly,

prob(3 people have different birthdays)

= 365 /365  × 364 /365 × 363 /365 ≈ 0.992.

prob(n people have different birthdays)

= 365 /365  × 364 /365 × 363 /365 ....... (366 − n) /365

can be written as  365!  / 365^n(365 − n)!