3. Conditional Probability. Assume that .05 percent of the population is sick with disease X. Doctors can check if a patient with an imperfect test. The test is 95% accurate when a patient has the disease, and 98 % accurate when a patient does not have the disease. If the test says that a patient has the disease, what is the probability that they are actually sick?

Suppose a math class contains 33 students. There are 23 females (five of whom speak Spanish) and 10 males (two of whom speak Spanish). Give all answers as decimals to at least two decimal places.   3. What percent of Spanish speaking students are male?   4. If someone does not speak Spanish what is the probability they are female?

Suppose 33.3% of high school students eat pizza and 42% drink soda. If 17.3% of high school students eat pizza and drink soda, what is the probability that a randomly chosen high student will either eat pizza, drink soda, or both?

In a certain high school, the probability that a student drops out is 0.1, and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.25. What is the probability that a randomly selected student gets a GED?