8. Examine the following table, concerning complaints received per week in a sto

Question

8. Examine the following table, concerning complaints received per week in a store. #complaints | 0 | 1-3 | 4-6 | 7-9 | 10-12 | Exceeds 12 Probability0.14 0.39 0.23 0.15 Let A be the event "There is at least one complaint in a week." Let B be the event "There are fewer than 10 complaints in a week." 0.06 0.03 What is the probability of the complement of A? What is the probability of the union of A and B? What is the probability of the intersection of A and B? Are A and B mutually exclusive? Are A and B exhaustive?

Explanation / Answer

The complement of A is "There are no complaints in the week". It's probability is 0.14.

Union of A and B is any number of complaints and it's probability is 1.

Intersection of A and B is "There is atleast one and atmost 9 compliants". It's probability is 0.39 + 0.23 + 0.15 = 0.77.

Since the probability above is not zero, A and B are not mutally exclusive.

Since the probability of the union of A and B is 1, they are exhuastive.

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