Assume 365 days per year. If 15 people are selected at random, what is the probability that at least two of them will have the same birthday?
The probability is =1 - [365P15 / 365^15] =
1 - [2.031285348831 x 10^38 / 2.7188983230290 x 10^38]
1 - 0.74709868 = 0.25290131 x 100 =25.29% - The probability that any two will share the same birthday.
The probability that at least two share a birthday is 1 - P( that none share a birthday )
And the probability that none share a birthday is given by :
[ 365 * 364 * 363 * .....* 352 * 351 ] / [ 350 ! * 365^15] =
[ 365 ! ] / [350 ! * 365^15] ≈ .747
So... 1 - .747 ≈ .253 ≈ 25.3%