The distributional pattern of pulmonated slugs inhabiting Libya was studied in the AIUB Journal of Science and Engineering (Aug. 2003). The number of slugs of a certain species found in the survey area was modeled using the negative binomial distribution. Assume that the probability of observing a slug of a certain species (say, Milax rusticus) in the survey area is .2. Let Y represent the number of slugs that must be collected in order to obtain a sample of 10 Milax rusticus slugs.
a. Give the probability distribution for Y as a formula.

b. What is the expected value of Y? Interpret this value.

c. Find P(Y = 25).