Question

In: Statistics and Probability

Given these facts: Using the case of testing women for breast cancer (*) 1% have breast...

Given these facts:

  • Using the case of testing women for breast cancer (*)
  • 1% have breast cancer
  • 99% don’t have breast cancer
  • Mammogram tests
  • In event of a woman with cancer
  • 80% of mammograms detect breast cancer when it is there (positive)
  • 20% miss it (false negative)
  • In event of no cancer
  • 9.6% of mammograms detect breast cancer when it’s not there (false positive)
  • 90.4% correctly return a negative result.

Questions:

  1. A lady takes the test three times and all three tests are positive. What are the chance of her having cancer?
  2. A lady takes the test, and it shows negative, but she is not convinced and so takes a second test. The second test is positive. What are the chances that she has cancer?
  3. A lady takes the test, and it shows negative, but she is not convinced and so takes a second test, which still shows negative. What are the chances that she has cancer?
  4. A lady takes the test, and it shows positive, but she is not convinced and so takes a second test. The second test is negative. What are the chances that she has cancer?

Solutions

Expert Solution


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