Municipal bonds issued throughout the United States, 60 percent were rates A, 30 percent B, and 10 percent C. O f the bonds rated A, 40 percent were issued by cities, 40 percent by suburbs and 20 percent by rural areas. Of the bonds rated B, 50 percent were from cities, 30 percent from suburbs and 20 percent from rural areas. Of the bonds rated C, 80 percent were from cities, 10 percent from suburbs and 10 percent from rural areas. A bond is selected at random.

a) What is the conditional probability of selecting a bond form a rural area, given that it is rated C?
b) What is the joint probability of selecting a bond rated C that is form a rural area?
c) What is the probability that the bond rated is C, given that it is from a rural area?