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?

Step-by-step explanation:

a. P(mites OR ticks) = P(mites) + P(ticks) − P(mites AND ticks)

P(mites OR ticks) = 0.80 + 0.30 − 0.20

P(mites OR ticks) = 0.90

b. P(no ticks | mites) = P(no ticks AND mites) / P(mites)

P(no ticks | mites) = (0.80 − 0.20) / 0.80

P(no ticks | mites) = 0.75

c. If two events are independent, then P(A and B) = P(A) × P(B).

P(mites AND ticks) = 0.20

P(mites) × P(ticks) = 0.80 × 0.30 = 0.24

They are not independent.

step-by-step explanation:

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