A genetic trait is often governed by a pair of genes, one inherited from each parent. The genes may be of two types, often labeled A and a. An individual then may have three different pairs: AA, Aa (which is the same as aA), or aa. In many cases the AA and Aa individuals cannot be otherwise distinguished; in these cases gene A is dominant and gene a is recessive. Likewise, an AA individual is called dominant and an aa individual is called recessive. An Aa individual is called a hybrid.

a. Show that if a dominant individual is mated with a hybrid, the probability of an offspring being dominant is 1=2 and the probability of an offspring being a hybrid is 1=2.


b. Show that if a recessive individual is mated with a hybrid, the probability of an offspring being recessive is 1=2 and the probability of an offspring being a hybrid is 1=2.


c. Show that if a hybrid individual is mated with another hybrid, the probability of an offspring being dominant is 1=4, the probability of an offspring being recessive is 1=4, and the probability of an offspring being a hybrid is 1=2.