1. A girl is concerned she might have a disease that affects 1% of the population. Luckily, a drug-store test is available. The test has a false- positive rate of 3% and a false-negative rate of 1% (a false positive is when a person doesn't have the disease, but the test result is positive). (a) What is the probability of a positive test result? (b) The girl takes the test, and it returns positive. Given this information, what is the probability that she has the disease? (c) The girl is aware that the test is imperfect, so she decides to take a second test. It also returns positive. Given the results of both tests, what is the probability that she has the disease? You may assume that the two test results are conditionally independent given her disease status. 2. Independent flips of a coin that lands on heads with probability 1/2 are made. What is the probability that the first four outcomes are (a) at least one T? (b) What is the probability that the pattern T, H, H, H occurs before the pattern H, H, H, H