Math 1307 Review for Test #2 Chapter 8—Probability: The Mathematics of Chance

1. A group of 100 people touring Europe includes 42 who speak French, 55 who speak German, and 17 who

speak both French and German.

  1. Draw a Venn diagram to help you organize this information.
  1. How many of these tourists speak neither French nor German?
  1. Find the probability that a tourist selected at random speaks either French or German.

2. A medical researcher classifies subjects according to male or female; smoker or nonsmoker; and

underweight, average weight, or overweight.

  1. Use a tree diagram to organize this information and determine the number of classifications that

are possible.

  1. Use the multiplication principle of counting to determine the number of classifications that are

possible.

3. A spinner with congruent regions numbered 1 through 4 is spun and a fair coin is tossed.

  1. Show the sample space for this experiment if the number spun is listed first and the side of the coin

is listed second.

  1. Suppose we have assigned a numerical value for the coin toss as follows: Heads = 2 and Tails = 1.

Set up a probability model for the sum of the number on the spinner and the value of the coin.

  1. Find the odds for the sum on the spinner and the coin is a prime number.

4. Three of six people are going to be chosen fro a committee. The positions on the committee will be:

Chair, Secretary, and Treasurer. In how many ways can these positions be filled?

5. A jewelry store with 8 stores in Georgia, 12 in Florida, and 10 in Alabama is planning to close 10 stores.

If they close 2 in Georgia, 5 in Florida, and 3 in Alabama, determine in how many ways this can be

done.

6. A four person committee is to be chosen from Department A and Department B. Department A has 15

employees and Department B has 20 employees.

  1. What is the probability of choosing 3 from Department A and 1 from Department B.
  1. Determine the odds for selecting 3 from A and 1 from B.

7. The weight of potato chip bags filled by a machine at a packaging plant is normally distributed with a

mean of 15.0 ounces and a standard deviation of 0.2 ounces.

  1. Find the probability that a bag chosen at random will weigh more than 15.2 ounces.
  1. Find the probability that a bag chosen at random will weigh less than 14.6 ounces.

8. The marketing department of an electronics manufacturer has done research on the number of television

sets owned by families in a certain town. The probability model for the number of sets owned by

randomly selected families is given below.

# TV sets 0 1 2 3

Probability0.04 0.340.470.15

  1. Find the mean number of sets per family in this town.
  1. Find the standard deviation.

9. In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation

of 0.002 mm. Each hour a sample of 20 ball bearings is chosen and the diameters are measured.

  1. Find the mean for the sample.
  1. Find the standard deviation for the sample.

10. A friend wants to play a game where you draw a card from a standard deck of 52. If you draw an Ace,

you win $20. If you draw a face card, you win $10. If you draw anything else, you must pay $5.

What is the expected value of this draw?