## MAT 131 Sample Test 4

1. A campus organization has 30 members including Alice, Bob, and Carla.

a. A slate of officers (president, vice-president, and secretary) is selected selected at random. How many different slates of officers are possible? What is the probability that Alice will be the candidate for president, Bob will be the candidate for vice-president, and Carla will be the candidate for secretary?

b. A committee of three is selected at random. How many different committees are possible? What is the probability that Alice, Bob, and Carla will be on the committee?

c. A committee of four is selected at random. How many different committees are possible? What is the probability that Alice, Bob, and Carla will be on the committee?

2. A monkey is given 7 wooden blocks with the letters "ABLLNOO" (one letter per block). If the monkey lines up the blocks randomly, what is the probability that the blocks would spell the word "BALLOON"?

3. An urn contains eight white balls and two green balls. A sample of three balls is selected at random without replacement.

a. Draw a tree diagram for this experiment.

b. Find the probability that all three balls will be white.

c. Find the probability that at least one ball will be green.

d. Find the probability that the third ball was white given that the first ball was green.

e. Find the probability that the first ball was white given that the third ball was green.

4. Repeat number three assuming that the sample is selected with replacement.

5. The table below gives the probability distribution of income levels and shows the proportion of families at each income level that own two or more cars.

 Annual Family Income Probability Proportion of Families with Two or More Cars ≤ \$30,000 0.10 0.20 \$30,000 to \$44,999 0.20 0.50 \$45,000 to \$59,999 0.35 0.60 \$60,000 to \$74,999 0.30 0.75 ≥ \$75,000 0.05 0.90

a. Draw the tree diagram for this table.

b. Find the probability that a randomly selected family has two or more cars.

c. Find the probability that a randomly selected family has two or more cars given that family income is greater than or equal to \$45,000.

d. Find the probability that a randomly selected family has an income between \$30,000 and \$59,999 given that it does not have two or more cars.

6. A men's soccer team plays 0, 1, or 2 games a week. The probability that they play 0 games is 0.2, the probability that they play 1 game is 0.5, and the probability that they play 2 games is 0.3. On average, how many games do they play per week?

7. A special six-sided die has one dot on one face, two dots on two faces, and three dots on three faces. In an experiment, two of these dice are rolled and the dot sum is found. What is the expected value for the dot sum?

8. On an Excel worksheet, simulate 500 spins of the spinner shown below, generate a column chart comparing the empirical and theoretical probabilities and find the expected value of an experiment consisting of a single spin of this spinner.

9. On an Excel worksheet, simulate 500 spins of the spinner shown below, generate a column chart comparing the empirical and theoretical probabilities and find the expected value of an experiment consisting of a single spin of this spinner.

Solutions