I'm having some trouble with these...
A test for Hepatitis A is 98% accurate: if a person has Hepatitis, the test will come out "positive" with 0.98 probability, and if a person doesn't have Hepatitis, the test will come out "negative" with 0.98 probability. The percentage of the population that has Hepatitis A is 0.005. Based on these probabilities, if a person tests positive for Hepatitis A, what is the probability that the person actually has Hepatitis A?
I got the answer for this by doing 0.98 * .005 = .0049, but it seems too easy of a calculation. Did I do this correctly?
The next problem says
Harry is an employee at a golf resort that has a couple of different courses. He's told by his owner to cut 10 greens and that he should spend only one hour on each green. For a par 3 green there is a 0.80 probability that he will cut it in one hour. For a par 5 green there is a 0.60 probability that he will have it cut in one hour. If his job is to prepare six par 3 greens and four par 5 greens, what is the probability that he will have at least 9 of them cut in the time given?
I tried a combinations of things for this problem like multiplying .80 with itself 6 times and adding that with (.60 * .60 * .60 * .60). It doesn't feel right though. Please get me headed in the direction