At any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited. If it is state 1 on one observation, then it is 3 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in state 2 on one observation, then it is 3 as likely to be in the state 2 as state 1 on the next observation. (a) If the particle is in state 1 on the fourth observation, what is the probability that it will be in state 2 on the sixth observation and state 1 on the seventh observation?

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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.

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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.