Draw a Venn diagram. Draw a Venn diagram that shows the relation between the events A and B in given Exercise. Indicate each of the following events on your diagram and use the information in given Exercise to calculate the probability of each event. Finally, describe in words what each event is.
(a) {A and B}
(b) {Ac and B}
(c) {A and Bc}
(d) {Ac and Bc}
Exercise
Education and income. Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated.
Suppose P(A) = 0.138, P(B) = 0.261, and the probability that a household is both prosperous and educated is P(A and B) = 0.082. What is the probability P(A or B) that the household selected is either prosperous or educated?