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)

0.11

0.15

0.20

0.25

0.19

0.07

0.03

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}