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In this question, we will apply Bayes' Theorem to determine the optimal policy for breast cancer screening, an important public health issue. Many physicians encourage women to have regular mammogram tests to detect breast cancer, so that the cancer can be treated before it spreads. Mammogram tests are very effective. For this question, we will assume that all mammogram test have a sensitivity rate of 90%, and a specificity rate of 90%. (Hint: Sensitivity is the probability for a person who has a disease to be correctly tested positive. Specificity is the probability for a person who does not have a disease to be correctly tested negative.)

In this question, we will apply Bayes' Theorem to determine the optimal policy for breast cancer screening, an important public health issue. Many physicians encourage women to have regular mammogram tests to detect breast cancer, so that the cancer can be treated before it spreads. Mammogram tests are very effective. For this question, we will assume that all mammogram test have a sensitivity rate of 90%, and a specificity rate of 90%. (Hint: Sensitivity is the probability for a person who has a disease to be correctly tested positive. Specificity is the probability for a person who does not have a disease to be correctly tested negative.)

A First Course in Probability (10th Edition)
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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2 questions, first one is (a) and the second one is (b)

In this question, we will apply Bayes' Theorem to determine the optimal policy for breast cancer screening, an important public health issue. Many physicians encourage women to have regular mammogram tests to detect breast cancer, so that the cancer can be treated before it spreads. Mammogram tests are very effective. For this question, we will assume that all mammogram tests have a sensitivity rate of 90%, and a specificity rate of 90%. (Hint: Sensitivity is the probability for a person who has a disease to be correctly tested positive. Specificity is the probability for a person who does not have a disease to be correctly tested negative.) In your own words, clearly explain the difference between false positive and false negative with an example. In your opinion, which diagnosis is worse for breast cancer: a false positive or a false negative? Explain.
Transcribed Image Text:In this question, we will apply Bayes' Theorem to determine the optimal policy for breast cancer screening, an important public health issue. Many physicians encourage women to have regular mammogram tests to detect breast cancer, so that the cancer can be treated before it spreads. Mammogram tests are very effective. For this question, we will assume that all mammogram tests have a sensitivity rate of 90%, and a specificity rate of 90%. (Hint: Sensitivity is the probability for a person who has a disease to be correctly tested positive. Specificity is the probability for a person who does not have a disease to be correctly tested negative.) In your own words, clearly explain the difference between false positive and false negative with an example. In your opinion, which diagnosis is worse for breast cancer: a false positive or a false negative? Explain.
The incidence rate of breast cancer is 0.4% in 30-year-old women, and 4.0% in 70-year-old women. If a woman receives a positive result on a mammogram, what is the probability that she indeed has breast cancer? Answer this question for both the 30-year-old and the 70-year-old.
Transcribed Image Text:The incidence rate of breast cancer is 0.4% in 30-year-old women, and 4.0% in 70-year-old women. If a woman receives a positive result on a mammogram, what is the probability that she indeed has breast cancer? Answer this question for both the 30-year-old and the 70-year-old.
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