2024 HCI J2 TPE Q10

In a survey on pet ownership with a large group of girls and boys in a primary school, \(\frac{1}{3}\) of the girls and \(\frac{5}{12}\) of the boys indicated that they own pets.

A pair consisting of one girl and one boy are chosen at random. It is given that if the girl owns pets, then the probability that the boy owns pets is \(\frac{5}{9}\).

1. Show that pet ownership between a pair of girl and boy is not independent.
   Give a possible reason, in this context, why this is so.[2]
2. Find exactly the probability that the boy owns pets, but the girl doesn't.[2]
3. Find exactly the probability that either the girl or the boy own pets, but not both.[2]