Question

Suppose that when a given parasite finds a host, there is a probability of 0.2 that the host already has eggs laid by a previous female. If the host is unparasitized, the female lays a male egg with the probability 0.05 and female egg with the probability of 0.95. If the host already has eggs, then a male egg is laid with the probability of 0.9 and a female egg with the probability of 0.1. Using this information, compute:

a.) The probability that the host is not already parasitized and the sex of the new egg is now male.

b.) The probability that the new egg is male.

c.) If the sex of a new egg is male, what is the probability that the host was parasitized?

Answer 1

Let Parasitized be denoted by "Pa".

Male is M and Female is F.

P(Pa)=0.2 So prob of unparasitized is P(UPa)=0.8

If the host is unparasitized, the female lays a male egg with the probability 0.05

P(M|UPa)=0.05

and female egg with the probability of 0.95

P(F|UPa)=0.95

If the host already has eggs, then a male egg is laid with the probability of 0.9

P(M|Pa)=0.9

and a female egg with the probability of 0.1.

P(F|Pa)=0.1

a.) The probability that the host is not already parasitized and the sex of the new egg is now male.

We know by Bayes theorem

So

b.) The probability that the new egg is male.

c.) If the sex of a new egg is male, what is the probability that the host was parasitized?

By Bayes Theorem