45. The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group–blood group combinations.

Suppose that an individual is randomly selected from the population, and define events by A
{type A selected}, B
{type B selected}, and C
{ethnic group 3 selected}.

a. Calculate P(A), P(C), and P(A C).

b. Calculate both P(A⏐C) and P(C⏐A), and explain in context what each of these probabilities represents.

c. If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1?