A batch contains 31 bacteria cells and 12 of the cells are not capable of cellular replication. Suppose you examine three bacteria cells selected at random, without replacement.
Round your answers to three decimal places (e.g. 98.765).
(a) What is the probability mass function of the number of cells in the sample, X, that can replicate?
f(X = 0) =
f(X = 1) =
f(X = 2) =
f(X = 3) =
(b) What is the mean and variance of the number of cells in the sample that can replicate?
Mean =
Variance =
(c) What is the probability that at least one of the selected cells cannot replicate?
Probability =