User blog:Tuner King 5/Help plz

“Suppose 30 people are in a room. What is the probability that two of them share the same birthday? Ignore the year of birth.”

Defining: n = number of people in a room P(A) = probability at least two people in the room have the same birthday P(A’) = probability at least two people in the room don’t have the same birthday therefore: P(A) = 1 - P(A’) We are taking into consideration leap years, so the number of days in a year will be 366 rather than 365

P(1’) = 366/366 = 1 so P(1) = 1 - 1 = 0

P(2’) = 366/366 x 365/366 = 0.9973 so P(2) = 1 - 0.9973 = 0.0027

P(3’) = 366/366 x 365/366 x 364/366 = 0.9918 so P(3) = 1 - 0.9918 = 0.0082

P(4’) = 366/366 x 365/366 x 364/366 x 363/366 = 0.9837 so P(4) = 1 - 0.9837 = 0.0163

Using these simple statistical calculations we can form a formula:



I have the derivative, but how do you solve for zero to get the max?