C. Bayes Rule 1. Two urns each contain a mix of red and green balls. Urn A has 75% red and the rest green. Urn B has 50% red and the rest green. You randomly select an urn and draw a red ball from it. What's the probability that you drew from urn A? That is what is P(A/R)? 2. 85% of the enemy planes in an area are Vietnamese and 15% are Cambodian. A pilot is shot down by a plane and the pilot is 80% accurate at identifying planes under the conditions of being shot down. (For example, if shown a Cambodian plane she correctly identifies it 80% of the time.) The pilot says the plane was a Cambodian plane; what's the probability she was right? That is, what is the probability the plane is Cambodian given that the pilot said it was? 3. You are worried about having a dangerous virus that affects one in a million people, and you decide to be tested. Given that you have the virus, the test will show positive with 99% probability. The test will show positive with only a 1% probability when given to a healthy person. (The false positive and false negative rate are the same at 1%.) What's the probability that you have the virus given that you test positive (with the 99% accurate test)