QMTH 205

Problem Set 2 Revised 2/28/2020

1. The following joint probability table shows household income by education level of the head of

household.

Education Level

Not HS Graduate

HS Graduate

Some College

Bachelor’s Degree

Beyond Bach. Degree

Total

Under 25

4,207

4,917

2,807

885

290

13,106

Household Income ($1000s)

25-49.9

50-74.9

75-99.9

100+

Total

3,459

1,389

539

367

9,961

6,850

5,027

2,637

2,668

22,099

5,258

4,678

3,250

4,074

20,067

2,094

2,848

2,581

5,379

13,787

829

1,274

1,241

4,188

7,822

18,490

15,216

10,248

16,676

73,736

a. What is the probability of a head of household not being a high school graduate?

b. What is the probability of a head of household having a bachelor’s degree or more education?

c. Given the head of household has a bachelor’s degree, what is the probability she earns $100,000

or more?

d. What is the probability of a household having income below $25,000?

e. Given the head of household has a bachelor’s degree, what is the probability he earns less than

$25,000?

f. Is household income independent of education level?

2. Based on weather data collected in Racine, Wisconsin on Christmas Day, the weather had the

following distribution:

Event

Relative Frequency

Clear and dry

0.20

Cloudy and dry

0.30

Rain

0.40

Snow

0.10

a. Based on the data in the table, what is the probability that next Christmas will be dry?

b. Based on the data, what is the probability that next Christmas will be rainy or cloudy and

dry?

c. Supposing next Christmas is dry, determine the probability that it will also be cloudy?

3.

Three events occur with probabilities of P(E1) = 0.35, P(E2) = 0.15, P(E3) = 0.40. If the event B

occurs, the probability becomes P(E1|B) = 0.25, P(B)=0.30.

a. Calculate P(E1 and B).

b. Calculate P(E1 or B).

c. Assume that E1, E2, and E3 are independent. Calculate P(E1 and E2 and E3).

QMTH 205

Problem Set 2 Revised 2/28/2020

4. Men have a reputation for not wanting to ask for directions. A Harris study conducted for

Lincoln Mercury indicated that 42% of men and 61% of women would stop and ask for

directions. The US Census Bureau’s 2007 population estimate was that for individuals 18 or over,

48.2% were men and 51.8% were women. This exercise addresses this age group.

a. A randomly chosen driver gets lost on a road trip. Determine the probability that the

driver is a woman and stops to ask for directions.

b. Calculate the probability that the driver stops to ask for directions.

c. Given that a driver stops to ask for directions, determine the probability that the driver

was a man.

5. With a single roll of a pair of dice, determine the probability of getting the following:

a. The sum of 7

b. The sum of 7 given that at least one of the dice is a 5.

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