An airport limousine can accommodate up to four passengers upon any one trip. The company will accept maximum of six reservations for a trip, and passenger should have a reservation. From previous records, 30% of all those making reservations don't appear for the trip. Answer the following questions, supposing independence wherever appropriate. (Round your answers to three decimal places.)
(a) If six reservations are made, determine the probability that at least one individual with a reservation cannot be accommodated on the trip?
(b) If six reservations are made, determine the expected number of available places when the limousine departs?
places
(c) Assume the probability distribution of the number of reservations made is given in the accompanying table.
| Number of reservations |
3 |
4 |
5 |
6 |
| Probability |
0.13 |
0.24 |
0.29 |
0.34 |
Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X.