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Conversation with Sharon

It’s Christmas time again and like we do every year, my home town friends are getting together to do secret santa and potluck dinner. So every year we get together around end of november to pick our secret santa. Since this year lot of the friends are out of town, we decided to use an existing online system instead of meeting up.

But the online system had a minor flaw. The online system allowed the members to pick the same person as last year. Normally this was resolved by redoing the drawing. This used to be easy when everyone was at the same place passing basket around to do the drawing, but now it’s felt more cumbersome to do again when doing it online.

Anyways, this is the email exchange regarding this issue:

Sharon Lee

ok so since most ppl don’t want to redraw the people that did want to will just have to deal with it

k bye peggy!

Timothy Kim

Even if you do a redraw, the probability that someone in the group getting the same person from last year is very high. So, I applaud Sharon’s decision

If you are wondering about the actual probability… here’s my quick math:

Given N number of people
Let n(i) denote the ith person in the drawing. So, n(1) means first person to draw.
Probability that n(i) picks the same person as before, denoted as P(n(i)) can be calculated as follows:

Let x(i) be the person that n(i) picked last year.
P(n(i)) = Probability that n(1) ~ n(i-1) didn’t pick x(i) AND n(i) will pick x(i)

This can be simplified to

P(n(i)) = (1 - P(one of n(1) ~ n(i-1) picked x(i)) ) * P(n(i) will pick x(i))
P(n(i)) = (1 - ( 1/N + 1/N-1 + … + 1/N-i+2)) * 1/N-i+1

… rest omitted for length

Sharon Lee

in light of tim’s excessive nerdiness i rescind my offer to tim for participating in secret santa

whoever got tim..congrats - you got a bye this year

^_^;; I love my friends~

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