A survey was taken among cola drinkers to see which of two popular brands people preferred. It was found that 45% liked brand A, 28% liked brand B, and 15% liked both brands. Suppose that a person in the survey is randomly selected. (a) Find the probability that the person liked brand A, given that he or she liked brand B. (b) Find the probability that the person liked brand B, given that he or she liked brand A. (a) The probability that the person liked brand A, given that he or she liked brand B is (Round to three decimal places as needed.) (b) The probability that the person liked brand B, given that he or she liked brand A is (Round to three decimal places as needed.)
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.
We have given that,
The probability of like brand A drink, P( A ) = 45% = 0.45
The probability of like brand B drink, P( B ) = 28% = 0.28
The probability of like brand A and brand B both drink, P( A and B ) = 15% = 0.15
Conditional probability formula,
P( A/B ) = P( A and B ) / P( B )
P( B/A ) = P( A and B ) / P( A )
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