(See, not all of my posts lately are about fantasy sports. (Oh wait, this one actually is if you notice the direct mapping.))
A science class has an even number of students (2n for some positive integer n) and a 50-50 male female ratio. Those students are assigned randomly into lab partnerships. (Process doesn't matter but if it helps you visualize: Pick two students at random - they're partners. Pick two more students at random from among the ones who are left. Repeat until the two remaining students become partners.)
As a function of n, how many male-female partnerships do we expect?
Posted by Matt Bruce at September 18, 2007 06:36 PMBased on a tip from a prodigious math talent on a math problem of my own last week...
EV(M/F partnerships) = EV(M1 matched w/ F) + EV(M2 matched w/ F) + ... + EV(M-subn matched w/ F)
=n * EV(M1 matched w/ F)
=n * (n / (2n -1))
It seems to work for n = 2 and 3, so I'm happy with it.
Posted by: ZD at September 18, 2007 11:14 PM