Using Bayes' theorem, calculate the probability that a person who has had a positive test for a disease actually has the illness. Typically the test gives a correct positive result 90.0% of the time when a person has the illness. and gives an incorrect positive result 1.0% of the time when the person does not. Assume that 0.3% of the population has the illness, and the person who is tested was selected at random without necessarily showing any symptoms. Give your answer as a percentage with one digit after the decimal point. How would your answer in the previous part change if only people who showed symptoms typical of the illness were tested. and why?

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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.