Question

Two organisms with genotype AaBbCcDdEE mate. these loci are all independent. What fraction? of the offspring will have the same genotype as the parents? 1) 3/4 2) 9/64 3) 1/16 4)4/3 5)1/4

Answer 1

The answer is 1/16.

There are 5 loci, and we need to look at them as independent units.
For example, let's take Aa:
Parental generation:    Aa       x       Aa

Offspring:              AA       Aa      Aa       aa

So, these two organisms will have 2 out of 4 offspring with the same genotype as parents.
Since 2/4 = 1/2, then 1/2 is a probability that parents with Aa genotype will have offspring with the same genotype as parents.

The same case is for other three heterozygous loci (Bb, Cc, and Dd).

The parents with genotype EE will have all offspring with the same genotype as parents, and the possibility is 4 out of 4, which is 4/4 = 1.

So, the possibility that all of these independent loci inherit together is the product of all independent possibilities for each locus:

$\frac{1}{2}$ × $\frac{1}{2}$ × $\frac{1}{2}$ × $\frac{1}{2}$ × 1 = $\frac{1}{16}$