need help with following **Problem 6)** One percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for noncarriers. Suppose that the test is applied independently to two blood samples of the same individual.a) What is the probability that both tests yield the same result? b) Given that the result of the first test is positive, what is the probability that the individual is a carrier? c) If both tests are positive, what is the probability that the individual is a carrier?

Conditional Probability: Let A and B be two events with P(A) > 0. Then the conditional…

Problem 6) One percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for noncarriers. Suppose that the test is applied independently to two blood samples of a same individual. a) What is the probability that both tests yield the same result? b) Given that the result of the first test is positive, what is the probability that the individual is a carrier? c) If both tests are positive, what is the probability that the individual is a carrier?

Problem 6) One percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for noncarriers. Suppose that the test is applied independently to two blood samples of a same individual. a) What is the probability that both tests yield the same result? b) Given that the result of the first test is positive, what is the probability that the individual is a carrier? c) If both tests are positive, what is the probability that the individual is a carrier?

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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need help with following

**Problem 6)** One percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for noncarriers. Suppose that the test is applied independently to two blood samples of the same individual.

a) What is the probability that both tests yield the same result?
b) Given that the result of the first test is positive, what is the probability that the individual is a carrier?
c) If both tests are positive, what is the probability that the individual is a carrier?

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