(a) Tom has a fair coin and a two-headed coin (a coin that both sides are heads) in his pocket. He selects one of the coins at random, and when he flips it, it shows heads. What is the probability that it is the fair coin? (b) Suppose that he flips the same coin a second time and again it shows heads. Now what is the probability that it is the fair coin?
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.
Given data:
The number of fair coins is F=1.
The number of the unfair coins is F'=1
The probability of choosing a fair coin is,
The probability of choosing an unfair coin is,
The probability of getting the head when a fair coin is tossed is,
The probability of getting the head when an unfair coin is tossed is,
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