One out of every one- thousand people have disease X. A new test for X is available, but it's not very accurate. If you have X, there is an 80% chance the test comes back positive and a 20% chance it comes back negative. If you don't have X, there is a 60% chance the test comes back negative and a 40% chance it comes back positive. Question: You are randomly chosen to be tested for X. Since the test is not very accurate, you are administered the test 10 times; assume the outcomes of these 10 tests are independent. Seven out of the 10 tests come back positive. Given these test results, what is the probability you have X?
Please show as much work as possible, and please do not skip steps. I really want to learn how to solve this, so if you use a axiom please include it.
Problem Statement:
One out of every one- thousand people have disease X. A new test for X is available, but it's not very accurate.
If you have X, there is an 80% chance the test comes back positive and a 20% chance it comes back negative. If you don't have X, there is a 60% chance the test comes back negative and a 40% chance it comes back positive.
Question:
You are randomly chosen to be tested for X. Since the test is not very accurate, you are
administered the test 10 times; assume the outcomes of these 10 tests are independent. Seven
out of the 10 tests come back positive. Given these test results, what is the
have X?
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