[Exer4-2] Exercise 13 of Book {Devore2017B} P.108
A mail-order computer 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 |
| $p(x)$ | .10 | .15 | .20 | .25 | .20 | .06 | .04 |
Calculate the probability of each of the following events.
- (a) $\{$ at most 3 lines are in use $\}$
- (b) $\{$ fewer than 3 lines are in use $\}$
- (c) $\{$ at least 3 lines are in use $\}$
- (d) $\{$ between 2 and 5 lines, inclusive, are in use $\}$
- (e) $\{$ between 2 and 4 lines, inclusive, are not in use $\}$
- (f) $\{$ at least 4 lines are not in use $\}$