Thread: Did I do this correctly?

There are 40 students in our combinatorics class. Use combinatorial principles to compute the probability that at least two people in class have the same birthday (assume 365 days in a year)...

100% * summation from i=2 to 40 of ((40 choose i) * (1/365)^i * (364/365)^(40-i))

is equal to (by the binomial theorem)

100% * ((1/365 + 364/365)^40 - (40 choose 0) * (1/365)^0 * (364/365)^40 - (40 choose 1) * (1/365) * (364/365)^39)

= .546%

Originally Posted by jmedsy

There are 40 students in our combinatorics class. Use combinatorial principles to compute the probability that at least two people in class have the same birthday (assume 365 days in a year)...

100% * summation from i=2 to 40 of ((40 choose i) * (1/365)^i * (364/365)^(40-i))

is equal to (by the binomial theorem)

100% * ((1/365 + 364/365)^40 - (40 choose 0) * (1/365)^0 * (364/365)^40 - (40 choose 1) * (1/365) * (364/365)^39)

= .546%

Check your answer here: Birthday problem - Wikipedia, the free encyclopedia

Am I right to say my calculation yields the odds of at least 2 people in a class of 40 having a birthday on one particular day of the year rather than having the same inexplicit birthday?

Regardless, that link was helpful, thank you.