4. Find the mean and variance for the sum of the number of spots rolled on two fair six-sided dice. 5. Basketball players in the NBA average about 75% success in free throws. If there are 23 free-throw attempts in a game, what is the probability that more than 20 are good? 6. Suppose a patient who has a medical condition takes a diagnostic test, which has a sensitivity of 80%. (a) If the test is given repeatedly n times, what is the probability that the patient tests positive for the first time on the n-th test? (b) What is the probability that the patient tests positive at least once in those n tests? (c) What is the expected number of times the patient would have to repeat the test before seeing a positive test result?