A bull might be a carrier of osteopetrosis marble bone disea

A bull might be a carrier of osteopetrosis (marble bone disease, assume two alleles in this locus), a recessive lethal condition. Twenty percent of all cows in the same heard are thought to be carriers of the osteopetrosis allele. Artificial insemination matings to randomly chosen cows have already produced 100 normal calves, and no homozygous recessive calves.

What is your level of confidence that the bull is not a carrier of the gene for osteopetrosis?

Solution

Osteopetrosis (OS) is a recessive mutation on a single cattle chromosome. All the possible outcomes obtained from possible matings are shown below:

a. Risk of having an OS calf if I breed an OS carrier cow to an OS carrier bull: Every time you breed a carrier to a carrier, you will obtain 25% risk of having a dead OS affected calf, 50% risk of otherwise appearing normal calf which carries OS mutation and 25% chances of normal appearing, non-carrier calves.

b. Breeding of OS carrier cow to a non-carrier bull: There will be zero chances of the OS affected calf and 50% chances of a carrier calf.

The above observation shows that the bull is a non-carrier.