It is estimated that 0.5 % of the population of a city has certain disease. A diagnostic test has a probability 0.95 of giving a positive result when applied to a person has the disease, and a probability 0.10 of giving a false positive result. Suppose that the test is now done to a person from the city. Calculate the following probabilities: (a) The probability that the test result will be positive; (b) The probability that given a positive result, the person has the disaese; (c) The probability that given a negative result, the person does not have the disease;

It is estimated that 0.5 % of the population of a city has certain disease. A diagnostic test has a probability 0.95 of giving a positive result when applied to a person has the disease, and a probability 0.10 of giving a false positive result. Suppose that the test is now done to a person from the city. Calculate the following probabilities: (a) The probability that the test result will be positive; (b) The probability that given a positive result, the person has the disaese; (c) The probability that given a negative result, the person does not have the disease;

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Concept explainers

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.

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It is estimated that 0.5 % of the population of a city has certain disease. A diagnostic test has

a probability 0.95 of giving a positive result when applied to a person has the disease, and a

probability 0.10 of giving a false positive result. Suppose that the test is now done to a person

from the city.

Calculate the following probabilities:

(a) The probability that the test result will be positive;

(b) The probability that given a positive result, the person has the disaese;

(d) The probability that the person will be misclassified

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