Some cell types in a tissue represent only a very small portion of the total cell population, such as hematopoietic stem cells in blood. Imagine that a particular cell type is present at a rate of 1 cell in 100, 000. (a) Under what conditions would it be appropriate to approximate the probability of the number of rare cell types in a sample of size N with a Poisson distribution? (b) If we are given a sample with 50, 000 cells, what is the probability of finding exactly 1 of these rare cells? (c) If we want to be 95% sure that we would have at least 1 rare cell in our sample, how many cells must we collect? Note: "95% sure" means that the probability of the event of interest is 0.95.