EG381: Week 4 Probability: Exploring Different Representations of Data

EG381: Week 4 Probability

Exercise 4.1

Finding Probability

1

Solve the following:

1. Refer to the sample data given below:

Results from Experiments with Polygraph Instruments

Did the Subject Actually Lie?

No (Did Not Lie) Yes (Lied)

Positive test result

(Polygraph test indicated that

the subject lied.)

15

(false positive)

42

(true positive)

Negative test result

(Polygraph test indicated that

the subject did not lie.)

32

(true negative)

9

(false negative)

a. If one of the responses is randomly selected, what is the probability that it is a false negative? Express the

answer as a decimal.

b. What does this probability suggest about the accuracy of the polygraph test?

EG381: Week 4 Probability

Exercise 4.1

Finding Probability

2

2. Refer to the table below, which summarizes results from a study on people who refused to answer survey

questions:

Age

18-21 22-29 30-39 40-49 50-59 60 and

over

Responded 73 255 245 136 138 202

Refused 11 20 33 16 27 49

Assume that one of the subjects is randomly selected. What is the probability that the selected person

refused to respond or is over 59 years of age?

EG381: Week 4 Probability

Exercise 4.1

Finding Probability

3

3. Use the data in the following table, which summarizes blood groups and Rh types for 100 subjects.

Group

O A B AB

Type Rh +

39 35 8 4

Rh – 6 5 2 1

If 3 of the 100 subjects are randomly selected, find the probability that they are all group B and type Rh – .

Assume that the selections are made with replacement.

Assume that the selections are made without replacement.

4. Find the number of different possible five-card poker hands by evaluating 52C5.

5. Use Internet resources to locate information about a state lottery. Use the combination formula C(n,r) to

calculate the total number of possible lottery tickets in the state (or nearest state). Include the lottery rules

and your calculation. Remember to cite the resources you use.