Odds of genetic occurance? I need help!?

Question

I need help from all you mathematicians and geneticists out there to make sure I get my calculations correct for a newsletter article. Here goes, one parent has dominant RR, the other recessive rr for trait #1, so the F1 generation all have Rr. Cross those and 1 in 4 (25%) of the the F2 will be recessive rr. With a second trait involved, say dominant AA and recessive aa, I believe the odds of an F2 being recessive rr-aa is 1 in 16. I think. Here's the tough part, with 14 traits involved, what would the odds be of getting a F2 recessive for all traits? Thanks!

Thanks a lot!

Thanks a lot!

Thanks a lot!

Answer 1

I believe an easy way you can look at this is by considering the following:

With one allele, the frequency of pure recessive is 1/4. With two alleles, it's 1/4 * 1/4 - 1/16.

So with 14 alleles it would be 1/4 times itself 14 times. Or (1/4)^14.
Or 1/268435456 1/((2n)^2) where n = the number of alleles.

Answer 2

Assuming all the genes assort independently, then the probability of rr from the Rr x Rr is 1/4, the probability of aarr from the AaRr x AaRr is 1/16. So, the probability involving 1 gene is (1/4)^1, the probability involving 2 genes is (1/4)^2, and so on, so the probability involving 14 genes is (1/4)^14 = 1/268435456. It is the probability of each independent occurrence occurring simultaneously and each independent occurrence has the probability of 1/4 of occurring, so it is 1/4 * 1/4 * 1/4 * [repeat 10 more times] * 1/4.