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?

Question

Emmett Haynes

Mathematics

11 February, 05:41

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?

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Answers (1)

Know the Answer?

Reid Travis · Answer 1

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.