Chicken eggs are usually either white or brown; the main pigment in brown shells is protoporphyrin IX, a precursor of heme. Some breeds of chicken are known for laying eggs in which the predominant pigment is biliverdin, which turns eggshells blue.

Consider a breed of undomesticated chicken in which genotype does not totally determine egg color. For this breed, genotype OO individuals produce blue eggs with probability 0.90, genotype Oo individuals produce blue eggs with probability 0.85, and genotype oo individuals produce blue eggs with probability 0.82; egg color is determined independently each time a chicken lays a new egg. On a collecting trip, you encounter a hen sitting on a nest with 7 eggs, 3 of which are blue. You are interested in capturing the chicken if there is a reasonable chance it is a genotype oo chicken. Based on previous studies of this particular population of chickens, it is thought that about 50% are genotype OO, 35% are genotype Oo, and 15% are genotype oo.

Your friend is of the opinion that the hen is almost certainly genotype oo, since so few of the eggs are blue and oo chickens have the lowest chance of laying blue eggs. Do you agree with their reasoning? Reference numerical results to support your argument and explain your reasoning.