A certain brand of dinner ware set comes in three colors: red, white, and blue. Twenty percent of customers order the red set, 45% order the white, and 35% order the blue. Let X = 1 if a randomly chosen order is for a red set, let X = 0 otherwise; let Y = 1 if the order is for a white set, let Y = 0 otherwise; let Z = 1 if it is for either a red or white set, and let Z = 0 otherwise. a) Let pX denote the success probability for X. Find pX. b) Let pY denote the success probability for Y. Find pY. c) Let pZ denote the success probability for Z. Find pZ. d) Is it possible for both X and Y to equal 1? e) Does pZ = pX + pY? f) Does Z = X + Y? Explain.
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 certain brand of dinner ware set comes in three colors: red, white, and blue. Twenty percent of customers order the red set, 45% order the white, and 35% order the blue. Let X = 1 if a randomly chosen order is for a red set, let X = 0 otherwise; let Y = 1 if the order is for a white set, let Y = 0 otherwise; let Z = 1 if it is for either a red or white set, and let Z = 0 otherwise. a) Let pX denote the success probability for X. Find pX. b) Let pY denote the success probability for Y. Find pY. c) Let pZ denote the success probability for Z. Find pZ. d) Is it possible for both X and Y to equal 1? e) Does pZ = pX + pY? f) Does Z = X + Y? Explain.
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