In kidney transplantations, compatibility between donor and receiver depends on such factors as blood type and antigens. Suppose that for a randomly selected donor from a large national kidney registry, there is a 10% chance that he or she is compatible with a specific receiver. Three donors are randomly selected from this registry. Find the probability that 0, 1, 2, or all 3 selected donors are compatible.
a. Do this by constructing the sample space and finding the probability for each possible outcome of choosing three donors. Use these probabilities to construct the probability distribution.
b. Do this using the formula for the binomial distribution.