MAT274 | Probability in Mathematics - Grand canyon university
- Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 9X percent reliable, (this means that the test will yield an accurate positive result in 9X% of the cases where the disease is actually present.) Gestational diabetes affects X+1 percent of the population in our patient’s age group, and that our test has a false positive rate of X+4 percent.(Use your knowledge of Bayes’ Theorem and Conditional Probabilities) to Compute the following quantities based on this new information.
a. If 100,000 people take the blood test, how many people that test positive will actually have gestational diabetes? b. What is the probability of having the disease given that you test positive? c. If 100,000 people take the blood test, how many people would test negative despite actually having gestational diabetes? d. What is the probability of having the disease given that you tested negative? e. Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted? Fill inthe conditional probability table here, then answer the questions in each part below. You need to fill out the table using the following format. For similar exercise problems, check Topic 2 homework No 38(4.3.13), 39(4.3.18), 40(4.3.23). Please remember that part a and c answers come directly from the table after filling out. Part b and d requires the conditional probability. You still need to use the numbers from the table. When you fill out the table, first start with Total for Disease using diabetes affects X+1 percent of the population in our patient’s age group. Then, you need to fill out the rest of the table. Positive Negative Total Disease No Disease Total 100,000 i. Answer part (a) here. ii. Answer part (b) here. iii. Answer part (c) here. iv. Answer part (d) here. v. Comment on part e)