Fred, after getting his positive result as in the previous question, is advised to get a second opinion. So he takes a second test, we the following characteristics:

• The test's sensitivity is 80% (i.e, false negative rate 0.2)
• The test's specificity is 90% (i.e., false positive rate 0.1)

If the second test comes back positive, what is the probability now that Fred has cancer? What does this result tell you about the importance of multiple independent tests, especially for rare or unlikely events?

Use three decimal points in your answer.

Suppose that Fred gets screened for a certain cancer, and gets a positive result. We know the following facts:

• In the population at large, 1/1000 people have that cancer
• The test's sensitivity is 90% (i.e., its false negative rate is 0.1)
• The test's specificity is 99% (i.e., its fale positive rate is 0.01)

Use Bayes' Law to calculate the probability that Fred has this type of cancer.

Round to 3 decimal points in your answer.