During frequent trips to a certain city a traveling sales person stays at hotel A 50%of the time, at hotel B 30% of the time, and at hotel C 20% of the time. When the salesperson checks in, there is some problem with the reservation 3% of the time at hotel A, 6% of the time at hotel B, and 10% of the time at hotel C. Suppose the salesperson travels to this city. a) Find the probability that the sales person stays at hotel A and has a problem with the reservation.
b) Give a frequency interpretation of the probability calculated in (a).
c) Find the probability that the sales person has a problem with the reservation.
d) Suppose that the salesperson has a problem with the reservation. Find the probability that the salesperson is staying at hotel A.
e) Let A be the event that the salesperson stays at hotel A and let B be the event that the salesperson has a problem with reservation. Are the events A and B independent? Justify your answer.