An automobile insurance company classifies applicants by their driving records for the previous three years. Let U = {all applicants}, A = {applicants who have caused accidents}, B = {applicants who have received speeding tickets}, C = {applicants who have been arrested for driving while intoxicated}. Suppose we are given the following information: 3 applicants have caused accidents, received speeding tickets and been arrested for driving while intoxicated. 31 applicants have caused accidents and received speeding tickets. 26 applicants have caused accidents and been arrested for driving while intoxicated. 9 applicants have received speeding tickets and have been arrested for driving while intoxicated. 63 applicants have caused accidents. 47 applicants have received speeding tickets. 57 applicants have been arrested for driving while intoxicated. There are 120 applicants total. (a)Describe the following set using set theoretic notation: {applicants who have not caused accidents and either received speeding tickets or have been arrested for driving while intoxicated} (b)Draw Venn diagram and shade the region represented by the above set. (c)What is the number of elements in the above set. Justify your answer by filling the number of elements in basic regions of the Venn diagram.

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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.