For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warranty.Relevant probabilities areP(A) = .75 P(B|A) = .9 P(B|A′) = .8P(C|A ∩ B) = .8 P(C|A ∩ B′) = .6P(C|A′ ∩ B) = .7 P(C|A′ ∩ B′) = .3a. Construct a tree diagram consisting of first-, second-, and third-generation branches, and place an event label and appropriate probability next to each branch.b. Compute P(A ∩ B ∩ C).c. Compute P(B ∩ C).d. Compute P(C).e. Compute P(A|B ∩ C), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased.
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.
For customers purchasing a refrigerator at a certain appliance store, let A be the
Relevant probabilities are
P(A) = .75 P(B|A) = .9 P(B|A′) = .8
P(C|A ∩ B) = .8 P(C|A ∩ B′) = .6
P(C|A′ ∩ B) = .7 P(C|A′ ∩ B′) = .3
a. Construct a tree diagram consisting of first-, second-, and third-generation branches, and place an event label and appropriate probability next to each branch.
b. Compute P(A ∩ B ∩ C).
c. Compute P(B ∩ C).
d. Compute P(C).
e. Compute P(A|B ∩ C), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased.
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