1- Four 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.)

2- Suppose that 90% of drivers are "careful" and 10% are "reckless." Suppose further that a careful driver has a 0.2 probability of being in an accident in a given year, while for a reckless driver the probability is 0.4. What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.)

3- You will take either a basket-weaving course or a philosophy course, depending on what your advisor decides. You estimate that the probability of getting an A in basket weaving is 0.85, while in philosophy it is 0.60. However, the chances of your advisor choosing the basket-weaving course is only 20%, while there is an 80% chance that he will put you in the philosophy course. What is the probability that you end up with an A? (Enter your answer to three decimal places.)

4- A box contains 4 white, 3 red, and 4 black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)

5- Use the given values to find the following. (Enter your answers as fractions.)

P(A) = 0.5,P(B) = 0.5,P(A B) = 0.3

(a)P(A given B)

(b)P(B given A)

6- The U.S. Senate consists of 100 members, 2 from each state. A committee of 8 senators is formed. What is the probability that it contains at least one senator from your state? (Round your answer to two decimal places.)

7- An elevator has 6 people and makes 8 stops. What is the probability that no two people get off on the same floor? (Enter your answer as a fraction.)

8- A box contains 6 red and 9 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.)

9- A college survey claimed that 64% of students took English composition, 45% took calculus, 15% took both, and 9% took neither. Show that these figures cannot be correct.

a- The real percentage that took both classes is 9, not 15% as claimed by the survey.

b- The real percentage that took neither class is 15, not 9% as claimed by the survey.

c- The real percentage that took both classes is 6, not 15% as claimed by the survey.

d- The real percentage that took neither class is 6, not 9% as claimed by the survey.

10- In a town, 36% of the citizens contributed to the Republicans, 48% contributed to the Democrats, and 15% contributed to both. What percentage contributed to neither party?

%

11- If a committee of 4 is to be chosen at random from a class of 10 students, what is the probability of any particular committee being selected? (Enter your answer as a fraction.)

a- What if the committee is to consist of a president, a vice president, a treasurer, and a secretary? (Enter your answer as a fraction.)