3. An art collector travels to art auctions once a month on the average. Each trip is guaranteed to produce one purchase. The time between trips is exponentially distributed. Determine a. The probability that no purchase is made in a 3-month period b. The probability that no more than 8 purchases are made per year. c. The probability that the time between successive trips will exceed 1 month. 4. The time between arrivals at E&L restaurant is exponential with mean 5 minutes. The restaurant opens for business at 11:00 A.M. Determine: a. The probability of having 10 arrivals in the restaurant by 11:b A.M. given that 8 customers arrived by 1 1:(1-8) A.M. b. If the last customer arrived at 11.25 A.M, find the probability that a new customers will arrive between 11:28 and 11:33 A.M.