Suppose you and a friend will be seated at a round table with three other people. (There are exactly five chairs at the table, equally spaced.) People will be seated at the table randomly. What is the probability that you and your friend will be seated together? Make sure to explain or show how you get your answer.
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.
Suppose you and a friend will be seated at a round table with three other people.
(There are exactly five chairs at the table, equally spaced.) People will be seated at
the table randomly. What is the probability that you and your friend will be seated
together? Make sure to explain or show how you get your answer.
Given data:
*Total number of persons sitting around a round table is .
If n persons are sitting around a round table, the number of ways in which the n persons can sit around the round table is
Thus,
Here, there are 5 persons sitting around the round table randomly, the total number of ways in which the 5 persons can be seated around the round table is,
But, here it is said that two persons (me & my friend) are seated together, thus in this case treat this two persons as a single persons thus there are total of 4 persons, the number of ways in which the 4 persons can be seated around the round table is,
But, the two persons treated as one person can be arranged in two ways.
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