You are heterozygous at locus A. Both of your alleles, A1 and A2, have a 10% allele frequency in the population. If you are one of 22 people in a room, how many people do you expect to share a locus A allele with?
I come up with 6.8, working like so:
22 people = 44 locus A alleles in the room = 4.4 A1 alleles and 4.4 A2 alleles at 10% frequency.
I have one of each, leaving 3.4 of each allele to the rest of the room. So, looking at both alleles, there are 6.8 shared alleles out there.
My answer assumes that these alleles are all in different people - I don't know how to account for the probability of someone else having two of them. So I know I am wrong already. Is that last step all I'm missing, or have I gone wrong in a more fundamental way?
(Context: This was a question on a grad-level immunology exam. None of us students could agree on the answer afterwards, and the confused wording (I rephrased it above) made us strongly suspect the professor doesn't have the right answer either, so we wanted to see what the answer actually is for when the exams are graded.)