Suppose that n people, enumerated as 1, 2, · · · , n, sit randomly around a circular table. What is the probability of 1, 2 sitting next to each others? Calculate your answer through two different solution methods, corresponding to the two ways in class that we found a similar probability when n people form a line.
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.
When no attention is given to the order of arrangement of selected objects, we get a combination. It is given by the formula,
Here, the objective is to find the probability of 1, 2 sitting next to each other.
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