1. Probability. The USI student council consists of 14 radicals and 11 socialists. A committee is formed by selecting 5 students at random. (a) Calculate the probability that there is at least one socialist in this committee. (b) Given that there is at least one socialist in this committee, then what is the probability that 3 of the committee members are socialists?

10. In a group of 60 employees, 25 are managers. If a team of 8 employees is randomly selected, what is the probability that exactly 3 of them are managers?

9. In a group of 30 people, 10 have blue eyes. If a committee of 5 people is randomly selected, what is the probability that exactly 2 of them have blue eyes?

5. A bucket contains 7 red balls, 8 green balls, and 5 black balls. If 4 balls are chosen randomly, find the probability that at least 1 of them is red. (6

If a committee of 3 is to be chosen at random from a class of 15 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.)

1. A bag contains 7 green marbles, 2 white marbles, and 3 red marbles. A marble is removed and then placed back in the bag, and a second marble is picked. What is the probability of drawing a green marble and then a red marble? (Enter your probability as a fraction.) 2. A large box of vegetables contains 3 tomatoes, 4 heads of lettuce, and 8 onions. A vegetable is chosen at random and then replaced in the box, and a second vegetable is picked. What is the probability of choosing a tomato and then an onion? (Enter your probability as a fraction.)

8. The composition of the 108th Congress is 50 Republicans, 48 Democrats, and 2 Independent. A committee on aid to higher education is to be formed with 3 Senators to be chosen at random to head the committee. Find the probability that the group of 3 consists of a. All Democrats b. One Democrat, one Republican, and one Independent