1. > Find Birthday Matches by Month (see cards) > Find at least one common aspect that you have as birthday mates. We will share these with the other groups. > Do any birthday month mates have the same day? (i.e., June 10 th )

2. Birthday Paradox Problem

4. Why ??? Intuitive Approach If there are 23 people in a room, then there are C(23, 2) pairs of dates. C(23, 2) = 23! 21!2! = 253 Pairs

5. Now the Heavy Stuff Find the probability that all the people in a room (“n”) have distinct birthdays. ____, ____, ____, ____,____,………_____ 1 364 365 363 365 362 365 361 365 1 st person 2 nd person 3rd person 4 th person 1 365 365 th person p(n) = 1(1 - ) (1 - )(1 - )…… (1 - ) = 1 365 2 n -1 365 3 365! 365 n (365 –n)!

6. Now the Complement!!! P(match)= 1 – p(n) P(match) = 1 - 365! 365 n (365 – n)! Try it for 23 people P(23) = 1 - 365! 365 23 (365 – 23)! ≈ 50 %