Question

Mary tests positive for a disease P(test is positive | disease) = 0.95 P(test is negative | no disease) = 0.90 Mary is a randomly chosen woman from a population in which 2.5% have the disease. Based on this information, what is the posterior probability (given the positive test result) that Mary has the disease? –Please round your answer to 2 decimal places, like 0.12

Name: mary tests positive for a disease ptest is positive disease 095 ptest is negative no disease 090 mary is a randomly chosen woman from a population in which 25 have the disease based on this 76006
Uploaded: 2023-03-09T17:57:10-08:00
Duration: 1 min 55 s
Channel: Manisha Sarker
Description: mary tests positive for a disease ptest is positive disease 095 ptest is negative no disease 090 mary is a randomly chosen woman from a population in which 25 have the disease based on this 76006

          Mary tests positive for a disease
P(test is positive | disease) = 0.95
P(test is negative | no disease) = 0.90
Mary is a randomly chosen woman from a population in which 2.5% have the disease.
Based on this information, what is the posterior probability (given the positive test result) that Mary has the disease? 
–Please round your answer to 2 decimal places, like 0.12

Added by Aaron J.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Manisha Sarker

03/09/2023

Step 1

The formula for Bayes' theorem is: \[ P(Disease | Positive) = \frac{P(Positive | Disease) \cdot P(Disease)}{P(Positive)} \] Where: - \( P(Disease | Positive) \) is the posterior probability we want to find. - \( P(Positive | Disease) \) is the probability of Show more…

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Mary tests positive for a disease P(test is positive | disease) = 0.95 P(test is negative | no disease) = 0.90 Mary is a randomly chosen woman from a population in which 2.5% have the disease. Based on this information, what is the posterior probability (given the positive test result) that Mary has the disease? –Please round your answer to 2 decimal places, like 0.12