A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.
| x |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
| p(x) |
0.10 |
0.15 |
0.20 |
0.25 |
0.20 |
0.05 |
0.05 |
Calculate the probability of each of the following events.
(a) {at most three lines are in use}
(b) {fewer than three lines are in use}
(c) {at least three lines are in use}
(d) {between two and five lines, inclusive, are in use}
(e) {between two and four lines, inclusive, are not in use}
(f) {at least four lines are not in use}