Probability Distributions and genetics. Many traits are controlled by a dominant gene, denoted by

a, and a recessive gene, denoted by

a. Suppose that two parents carry these genes in the proportion 3:1; that is, the probability of either parent giving the a gene is 0.75, and the probability of either parent giving the a gene is 0.25. Assume that the genes are selected from each parent randomly. To answer the following questions, imagine 100 trial “births.”

a. What is the probability that a child receives an a gene from both parents?

b. What is the probability that a child receives an a gene from one parent and an a gene from the other parent?
Note that this can occur in two ways.

c. What is the probability that a child receives an a gene from both parents?

d. Make a table showing the probability distribution for all events.

e. If the combinations aa and aa both result in the same dominant trait (say, brown hair) and aa results in the recessive trait (say, blond hair), what is the probability that a child will have the dominant trait?