Suppose 10% of the population of WVU students has tested positive for COVID-19, W1 represents the part of the population that has tested positive and W2 represents those who tested negative. X denotes a test result that the person has tested positive for COVID-19. P(W1) = 0.10 individual tested positiveP(W2) = 0.90 Individual tested negativeP(X|W1) = 0.80 test shows the individual tested positive and is correctP(X|W2) = 0.30 test incorrectly shows the individual is positiveRandomly select an individual and preform the test. The result shows the person tested positive, what is the probability that the test is correct? Use Bayes' theorem to solve.

Given that P(W1) = 0.10, P(W2) = 0.90 P(X | W1) = 0.80, P(X | W2) = 0.30

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The result shows the person tested positive, what is the probability that the test is correct

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Suppose 10% of the population of WVU students has tested positive for COVID-19, W₁represents the part of the population that has tested positive and W₂ represents those who tested negative. X denotes a test result that the person has tested positive for COVID-19.
P(W₁) = 0.10 individual tested positive
P(W₂) = 0.90 Individual tested negative
P(X|W₁) = 0.80 test shows the individual tested positive and is correct
P(X|W₂) = 0.30 test incorrectly shows the individual is positive
Randomly select an individual and preform the test. The result shows the person tested positive, what is the probability that the test is correct? Use Bayes' theorem to solve.

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