Why is my cat orange?

One of the students in my Bayesian statistics class, Mafalda Borges, came up with an excellent new Bayes theorem problem.  Here's my paraphrase:

About 3/4 of orange cats are male.  If my cat is orange, what is the probability that his mother was orange?

To answer this question, you have to know a little about the genes that affect coat color in cats:

The sex-linked red gene, O, determines whether there will be red variations to fur color. This gene is located on the X chromosome...Males have only one X chromosome, so only have one allele of this gene. O results in orange variations, and o results in non-orange fur.Since females have two X chromosomes, they have two alleles of this gene. OO results in orange toned fur, oo results in non-orange fur, and Oo results in a tortoiseshell cat, in which some parts of the fur are orange variants and others areas non-orange.
If the population genetics for the red gene are in equilibrium, we can use the Hardy-Weinberg principle.  If the prevalence of the red allele is p and the prevalence of the non-red allele is q=1-p:

1)  The fraction of male cats that are orange is p and the fraction that are non-orange is q.

2) The fractions of female cats that are OO, Oo, and oo are p², 2pq, and q², respectively.

Finally, if we know the genetics of a mating pair, we can compute the probability of each genetic combination in their offspring.

1) If the offspring is male, he got a Y chromosome from his father.  Whether he is orange or not depends on which allele he got from his mother:
 

2) If the offspring is female, her coat depends on both parents:

That's all the background information you need to solve the problem.  I'll post the solution next week.