3. A state government issues bonds for the development of Cities, Suburban Areas, and Rural Areas in proportion of 50%, 30%, and 20% respectively. Of the bonds for cities, 60 % are of A grade, 40% are B grade. Of the bonds for Suburban Areas, 50% are A grade and 50% are B grade. Of the bonds for Rural Areas, 30% are A grade and 70% are B grade. a. Draw a tree diagram that depicts this scenario, and compute the probabilities at the end of the tree and name them. (Note that there are 6 branches at the end). (20) b. Make a contingency table and show the relevant probabilities. (Refer to the examples) (10) c. Compute the following probabilities: (30) i. Prob (A), Prob (B) ii. Prob (Cities|A), Prob (Cities B), Prob (Suburban |A), Prob (Rural |A) Prob(Suburban B), Prob(Rural B)