Is there a difference between the theoretical probability of a child being affected by an autosomal recessive disease carried by both of her parents (as in Question 1), and the fraction of affected children you observe when generating a random family with four children from those parents? If so, what can explain this discrepancy?

No difference

Explanation:

First, let us calculate the probability of a child being affected by an autosomal recessive disease carried by both of her parents. The parents are heterozygous (carriers). Assuming the allele for the disease is a, their genotypes would be Aa.

Crossing Aa and Aa:

           Aa   x   Aa

     AA   Aa   Aa   aa

The theoretical probability of a child being affected is 1/4.

From the cross as well, the fraction of affected children from a random generation of a family with four children from the carrier parents is also 1/4.

Hence, there is no difference between the two probabilities.

c) 50% there are four chromosomes. after crossing over, 2 of the four have been changed. that means any gamete has a 2 in 4 chance or 50% chance of receiving the mutated chromosome.