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 “there will be at least one complaint in a week” and B the event “there will be fewer than ten complaints in a week.”Number ofcomplaints 0 1 to 3 4 to 6 7 to 9 10 to 12 More than 12Probability 0.14 0.39 0.23 0.15 0.06 0.03a. 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?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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
Number of
complaints 0 1 to 3 4 to 6 7 to 9 10 to 12 More than 12
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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