Part 1. Two people , S and T, agree to meet at a restaurant. Each person will arrive, independently of the other, at 1:00. 1:30, or 2:00 p.m. Assume that each person has a probability of 1/3 of arriving at any of the three times. Find the probability that (show all work and justification):

(a) They both arrive at 1:30.

(b) They both arrive at the same time.

Part II. A survey was taken of 150 residents of a small resort town to determine their attitudes toward a proposed hotel development. The occupations of the residents were determined along with whether they approved of the hotel being built. The results are:

	Building and Trade	Businessmen	Other
Approve	40	40	5
Disapprove	10	20	35

(a) Find the proportions of the 150 residents who:

(a) Are businessmen

(b) Approve of the hotel being built

(c) Approve of the hotel being built, given that they are in the building and trade

(d) Are businessmen, given that they approve of the hotel being built

(e) Are businessmen or approve of the hotel being built

(f) Are the events "Businessmen" and "Approve" independent? Explain. Are they mutually Exclusive? Explain