1. If a committee of 3 is to be chosen at random from a class of 14 students, what is the probability of any particular committee being selected? (Enter your answer as a fraction.) What if the committee is to consist of a president, a vice president, and a treasurer? (Enter your answer as a fraction.) 2. In a town, 32% of the citizens contributed to the Republicans, 44% contributed to the Democrats, and 14% contributed to both. What percentage contributed to neither party? 3. A box contains 5 red and 6 green marbles. You reach in and remove 3 marbles all at once. (a) Find the probability that these 3 marbles are all red. (Enter your answer as a fraction.) (b) Find the probability that these 3 marbles are all of the same color. (Enter your answer as a fraction.) 4. An elevator has 5 people and makes 9 stops. What is the probability that no two people get off on the same floor? (Enter your answer as a fraction.) 5. The U.S. Senate consists of 100 members, 2 from each state. A committee of 6 senators is formed. What is the probability that it contains at least one senator from your state? (Round your answer to two decimal places.) 6. Use the given values to find the following. (Enter your answers as fractions.) P(A) = 0.7, P(B) = 0.3, P(A B) = 0.2 (a) P(A given B) (b) P(B given A) 7. Use the given value to find the following. (Enter your answers as fractions.) P(A) = 0.3, P(B) = 0.4, P(A B) = 0.5 (a) P(A given B) (b) P(B given A) 8. Suppose that 80% of drivers are "careful" and 20% are "reckless." Suppose further that a careful driver has a 0.1 probability of being in an accident in a given year, while for a reckless driver the probability is 0.3. What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.) 9. Two students are registered for the same class and attend independently of each other, student A 80% of the time and student B 70% of the time. The teacher remembers that on a given day at least one of them is in class. What is the probability that student A was in class that day? (Round your answer to three decimal places.) 10. Five dice are rolled. (a) Find the probability of getting all sixes. (Enter your answer as a fraction.) (b) Find the probability of getting all the same outcomes. (Enter your answer as a fraction.) (c) Find the probability of getting all different outcomes. (Enter your answer as a fraction.)