Question: A corporation takes delivery of some new machinery that must be installed and checked before it comes available. The corporation is sure that it will take no more than 7 days for this installation and check to take place. Let A be the event "It will be more than 4 days before the machinery becomes available" and B the event "It will be less than 6 days before the machinery becomes available"

(a) Are A and B mutually exclusive?

(b) Are A and B collectively exhaustive?

(c) If P(A)=0.5 and P(B)=0.7 calculate P(AÇB)

(d) (Optional) If it is given that the new machinery came available in less than 6 days what is the probability that it took more than 4 days?