> 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 )

Birthday Paradox Problem

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

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

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