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.

y 45 46 47 48 49 50 51 52 53 54 55 p(y) .05 .10 .12 .14 .25 .17 .06 .05 .03 .02 .01 x 0 1 2 3 4 5 6 p(x) .10 .15 .20 .25 .20 .06 .04

a. What is the probability that the flight will accommodate all ticketed passengers who show up?

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}