One of the three people in a group comes home with measles. Each of the other two people has a probability θ of catching measles from one who is infected. If neither or both get the measles, the epidemic ends.

However, if only one of them gets the disease, the remaining person has another opportunity θ, of being infected.

Let X be the total number of people who are infected before the epidemic

ends.

Show that

P(X=1) = (1 - θ)^2

P(X=2) = 2θ.(1 - θ)^2

P(X=3) = θ^2.(3-2θ)

Can anyone help me to start off?