3.3. In a transportation system having the network shown below, a sequence of passenger arrivals occurs at terminal 3. It is known that the arrivals' desired destinations are independently distributed with probability: 10 06 3 4 05 20 Fig. P3.3 pi = P[arrival has destination (] = 0.2 i = 1, 2, 4, 5, 6 (o) What is the PMF of the number of arrivals before the first appearance of a passenger wanting to go to destination (b) Suppose there is a vehicle waiting with five remaining seats with the operating rule that it will leave for station 4 when it is full or at the latest after the next seven arrivals. What is the probability the seats will be filled if station-4 travelers are the only ones accepted? (c) Suppose the vehicle described in part (b) will accept travelers to terminals 4, 5, or 6 instead of just 4. What now is the probability it will be full after seven more arrivals (or before)