Question

1. An aquarium contains Drosophila fruit flies: 8 D. melanogaster, 6 D. immigrans, and 4 D. simulans. Six flies are randomly taken from the aquarium.
   1. What discrete probability distribution best describes the probability of selecting specific numbers of flies from each species? Name the distribution and write down the equation (with all parameters assigned).
   2. Find the probability that 2 D. melanogaster, 2 D. immigrans and 2 D. simulans flies are selected
2. After 48 hours of hosting an infected deer tick in the nymph stage, the probability that a canine host contracts Lyme disease is 0.2. Nine dog hosts are randomly examined. Let X = the number of infected dogs.
3. 1. Find the probability that the first infected dog is the fifth dog to be examined.
   2. 1. Find the probability that the second infected dog is the fifth dog to be examined.
      2. Find the probability that the second infected dog is the fifth dog to be examined.

Answer 1

a) The probability distribution that best describes the probability of selecting specific numbers of flies from each species is multivariate hypergeometric distribution.

Let X,Y and Z be the number of melanogaster, immigrans and simulans respectively when we select 6 flies from the lot.

So,

b)