2. A large fruit-eating bat called the black flying fox, Pteropus alecto, occupies a large mangrove swamp on Indooroopilly Island. Assume that 80% of these bats are infected with an ectoparasitic mite and 30% have larger tick parasites. Twenty percent are infected with both.

a. Find the probability that a randomly chosen bat will have some parasites (mites or ticks).

b. If a randomly chosen bat has mites, what is the probability that it will not have ticks?

c. Are the presence of the two types of ectoparasites independent of each other?