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 in state 1 on the 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 the state 2 on one observation, then it is 3 as likely to be in state 2 as state 1 on the next observation. (a) If the particle is in state 1 on the first observation, what is the probability it is in state 1 on the fourth observation? (b) If the particle is in state 2 currently, what is the probability that it will be in state 2 then state 1 then state 1 then state 2 on the next four observations? (c) 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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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.