Finite Analysis PROF DOUBLE R

1. -/2 pointsBerrFinMath1 5.3.001.

Find the sample space for a committee of two chosen from Alice (A), Bill (B), Carol (C) and David (D).

O{(

O{(A, B, C, D)}

O{(

O{(

Find the sample space if both sexes must be represented.

O{A,B,C,D}

O{(

O{(

O{(

2. Two dice are rolled. E is the event that the sum is even, F is the event of rolling at least one six, and G is the event that the sum is eight. List the outcomes for the following events:

3. If a committee of 3 is to be chosen at random from a class of 12 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.)

4. In a town, 38% of the citizens contributed to the Republicans, 42% contributed to the Democrats, and 11% contributed to both. What percentage contributed to neither party?

5. -/2 pointsBerrFinMath1 5.3.007.

A box contains 4 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.)

6. -/1 pointsBerrFinMath1 5.3.008.

An elevator has 4 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.)

7. The U.S. Senate consists of 100 members, 2 from each state. A committee of 9 senators is formed. What is the probability that it contains at least one senator from your state? (Round your answer to two decimal places.)

8.

9. -Use the given value to find the following. (Enter your answers as fractions.)

10. A box contains 5 white, 2 red, and 5 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.)

11. Suppose that 70% of drivers are "careful" and 30% are "reckless." Suppose further that a careful driver has a 0.3 probability of being in an accident in a given year, while for a reckless driver the probability is 0.5 What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.)

12.-

Two students are registered for the same class and attend independently of each other, student A 70% of the time and student B 60% 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.)

13. For the experiment of tossing a coin twice, find whether events

A: heads on the first toss

B: different results on the two tosses are independent or dependent.

O independent

O dependent

14.- 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.)