3.5 A corporation takes delivery of some new machinery that must be installed and checked before it becomes available to use. The corporation is sure that it will take no more than 10 days for this installation and check to take place. Let A be the event

“it will be more than 3 days before the machinery becomes available” and B be the event “it will be less than 7 days before the machinery becomes available.”

a. Describe the event that is the complement of event A.

b. Describe the event that is the intersection of events A and B.

c. Describe the event that is the union of events A and B.

d. Are events A and B mutually exclusive?

e. Are events A and B collectively exhaustive?

f. Show that 1A  B2  1A  B2 = B.

g. Show that A  1A  B2 = A  B.