How many people must be in room before the probability that someone shares a birthday, ignoring the year and ignoring the leap years, becomes at least 50%?
This problem is known as the Birthday Paradox.
By Hand it's easier to compute the probability that there are no common birthdays.
1. Start by considering two students. There are 365 days the first student's birthday could land on and 364 days the second student's birthday could land on and not match the first student.
2. So the probability of no common birthday for 2 students is (365 x 364) / (365 x 365) = 0.99726. You could continue this process by adding students until you arrived at about a 50% chance of no common birthday which subtracted from one would mean there would be a 50% of having a common birthday. This could be a tedious process so...
3. There are two ways to work this problem on the calculator....TABLE function and RECURSION function.
4. Now lets check this paradox on a few Major League Baseball rosters. Did you find any matches?
http://mlb.mlb.com/team/roster_40man.jsp?c_id=atl
http://texas.rangers.mlb.com/team/roster_40man.jsp?c_id=tex
http://newyork.yankees.mlb.com/team/roster_40man.jsp?c_id=nyy
5. These are the 40-man rosters so what is the probability that there will be two people with the same birthday?
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