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.

Blood Group O A B AB 1 .082 .106 .008 .004 Ethnic Group 2 .135 .141 .018 .006 3 .215 .200 .065 .020 Small Medium Large Regular 14% 20% 26%
Decaf 20% 10% 10%
Suppose that an individual is randomly selected from the population, and define events by , , and .

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

b. Calculate both and , 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?