Question

# Many people think that everyone should be tested for the virus. However, it is generally a...

Many people think that everyone should be tested for the virus. However, it is generally a bad idea to do mass screening of an entire population, due to the risk of false positives. The most important example of this is that many women are no longer recommended to have annual mammograms to detect breast cancer. A mammogram has a false positive rate of about 9 percent. This means that assuming a woman is healthy, a mammogram will still come back positive 9 percent of the time. False positives cause anxiety, invasive tests, and other significant health problems.

3a. Assuming a woman is healthy, if they have ten annual mammograms, what is the probability that all of them correctly come back negative?

3b. Assuming a woman is healthy, if they have ten mammograms, what is the probability that at least one is a false positive?

When choosing a random woman, denote the following events with these letters:

H: The woman is healthy.

C: The woman has breast cancer.

N: The test comes back negative.

Y: The test comes back positive.

3c. Find P(N | H).

3d. Find P(Y | H).

3e. What does it mean that P(N | C) = 0.13?

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