For the following questions, you may use either a non-simulation or simulation approach (R code). Be sure

to clearly show your work and define any notation that you introduce in your solution.

Night blindness refers to an inherited condition characterized by impaired vision in dark conditions; in dim light or darkness, affected horses experience loss of vision. Night blindness is thought to be associated with genes involved in producing the spotted coat

pattern in Appaloosas.

Suppose that among Appaloosas that have gen AA and display spotting, night blindness

occurs with probability 0.45; among Appaloosas that have gen AA and do not display spotting, night blindness occurs with probability 0.08. About 9% of all Appaloosas are gen Aa, display spotting, and have night blindness. In Appaloosas that are gen aa and display spotting, night blindness occurs with probability 0.12; 1% of Appaloosas that are gen aa and do not display spotting have night blindness.

Let B represent the event that an Appaloosa has night blindness.

i. Calculate the probability that a randomly selected Appaloosa is geno AA and has

night blindness.

ii. Given that an Appaloosa is geno AA and has night blindness, what is the probability

that it exhibits spotting?

iii. If an Appaloosa is spotted and known to be geno Aa, what is the probability that it

does not have night blindness?

iv. What is the probability that an Appaloosa has night blindness, if it is known to be

geno aa?