A box of 200 light bulbs contains 80 bulbs that are defective. A sample of 20 bulbs is chosen at random. What is the probability that a sample will have exactly 2 defective bulbs? What is the probability that there is at least one defective bulb?

A new test for a disease gives the correct results 80% of the time for healthy people and gives the correct results 40% of the time for people with the disease. 20 percent of the entire population has the disease. A randomly chosen person is tested and the test results are either negative or positive. Find the probability that the person has the disease or doesn't have the disease.

Feel free to use calculator functions such as binomcdf or binompdf or anything you see fit.