A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the following table. Let A be the event €œthere will be at least one complaint in a week€ and B the event €œthere will be fewer than ten complaints in a week.€

a. Find the probability of A.
b. Find the probability of B.
c. Find the probability of the complement of A.
d. Find the probability of the union of A and B.
e. Find the probability of the intersection of A and B.
f. Are A and B mutually exclusive?
g. Are A and B collectively exhaustive?

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More complaints 01 to3 4 to 6 7to9 10 to 12 than 12 Probability 0.14 0.39 0.23 0.15 0.06 0.03