The negative binomial distribution was used to model the distribution of parasites (tapeworms) found in several species of Mediterranean fish (Journal of Fish Biology, Aug. 1990). Assume the event of interest is whether a parasite is found in the digestive tract of brill fish, and let Y be the number of brill that must be sampled until a parasitic infection is found. The researchers estimate the probability of an infected fish at .544. Use this information to estimate the following probabilities:
a. P(Y = 3)
b. P(Y ≤ 2)
c. P(Y> 2)