1. Let A and B be independent events. If P(A B) = 0.36 and P(A) = 0.84, calculate P(A B).

2. Instead of NBA star LeBron James, our free-throw shooter this time is Jack Stevens who manages to convert only 42.0% of all his free-throw attempts. For Jack's next four attempts, compute the probability of each event. Assume that converting or missing a free throw will have no effect on subsequent attempts. Three decimal places.

(a) he misses all four attempts.

(b) he converts at least three of these four attempts.

3. A rare disease is known to afflict about 1 in 300 people. A blood test for the disease has been developed but it is not perfect. If a subject has the disease, there is a 95% probability that the test result will be positive. If a subject does not have the disease, there is a 90% probability that the test result will be negative. Frodo's test result was positive. What is the probability that Frodo has the disease?