Please read the additional materials and answer the questions. Thank you Following don’t read. (Please see the attached writeup. It should not be too long to do. However, if you have questions regarding the translation of English to probability notation, please put it up on discussion so everyone can talk about the best way to make the translation. This is an important skill to have, especially when we get to chapter 4 use of Bayes’ rule to update prior probabilities. )

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Ch 2, Probability and Bayes’ Rule

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BUS 190

HW 8 Probability

Passenger vehicle drivers in fatal crashes by age and crash type, 2015

Single vehicle

Multiple vehicle

Age

Number

Number

16-19

1,256

1,642

20-24

2,375

2,838

25-29

1,863

2,514

30-59

6,511

11,112

60-69

1,334

2,554

70+

1,193

2,700

1. Above are the frequencies of drivers of passenger vehicle drivers who were involved in fatal

accidents by age, for the year 2015.

LEAVE ALL YOUR WORK AS FRACTIONS SO I CAN SEE WHERE YOU ARE GETTING YOUR

NUMBERS FROM. DO NOT REDUCE!

a. Write down all the marginal totals and the grand total above. (10 pts) (Give one example

calculation for the rows and one for the columns)

For the following use S for single vehicle, M for multiple vehicle, and the age group appended to a

variable Age (i.e., Age16-19, Age20-24, etc.) for the age categories.

Write out the probability being asked for IN NOTATION using the notation above, then give the answer,

leaving the numerator and denominator in fractions. SHOW YOUR WORK. DONT REDUCE THE

FRACTIONS.

b. What is the chance a driver involved in a fatal accident in 2015 is 16-19 years old? (2 pts.)

c. What is the chance a driver involved in a fatal accident was involved in a single vehicle accident?

(2 pts.)

d. What is the chance that a driver involved in a fatal accident was 16-19 years old AND involved n

a single vehicle accident? (show work, leave as fraction). (2 pts. )

e. What is the chance that a driver involved in a fatal accident was 16-19 years old OR involved in a

single vehicle accident? (show work, leave as fractions). (6 pts.)

f.

Given a driver was involved in a single vehicle fatal accident, what is the chance s/he was 16-19

years old?(HINT: CONDITIONAL) (2 pts.)

g. What is the chance that a driver aged 16-19 years old who was involved in a fatal accident was

involved in a single vehicle fatal accident? (HINT: CONDITIONAL) (2 pts.)

h. Are age and type of accident (single or multiple vehicle) independent? (You only have to

show the proper relationship holds for one cell the rest fall into place.) State which

criterion you are using to show it.

2. Practicing identification and notation for unconditional and conditional probabilities

Write the following in proper notation for either unconditional or conditional probability.

You are a marketing researcher. Your population is the customers for your company. You are

interested in the following demographics (with the notation you are to use following)

Female = F

Male = M

Marital Status = S (for status)

Annual income level between $50K and $75: I_50_75

Age between 18 and 24: A_18_24

You will NOT have numbers for the probabilities below just write the English statement in

probability notation, using the notation for events given above.

a. Probability that a randomly selected customer is between 18 and 24 years of age

b. Probability that a female customer being between 18 and 24 years of age

c. Probability that a customer who is between 18 and 24 years of age is female?

d. Probability that a customer makes between $50K and $75K inclusive, per year?

e.Probability, given a married male customer, what is the chance he makes between $50K

and$75K inclusive, per year?

f. Probability that a married female customer makes between $50K and $75K inclusive, per year

(you can use &, or, etc in describing someone)

3. You own and run a retail clothing store and want to see what is selling or not. Write out the

following in probability notation using the notation for the events given below. Put the given

numbers to your probabilities as appropriate. Your sales are split 50-50 between mens and

womens clothing.

Notation: W for womens garments

M for Mens garments

L for Large size garment

P for Pink garment

a.

25% of your sales are of large size garments.

b.

If a sale is of a large-size garment, the chance it is a mens garment is 60%.

c. If a sale is of a womans garment, the chance it is large size is 30%.

d. . When a sale is of a pink garment, the chance it is a womens garment is 90%.

e.

If a sale is of a womens garment, the chance it is pink is 10%.

f.

The chance a garment sold is pink is 3%.

g. For the questions above is your population customers or garments sold?

4. Bayes Rule

Dana is afraid that she will fail her QBA final, given her current grade. She believes that if she does not

find a tutor to help her, her chance of failing is 40%. However, if she does find a tutor, her chance of

failing drops to 10%. However, it is late in the semester, and she believes the chance she will be able to

find a tutor to help her is only 50%.

If Dana fails the final, what is the chance she had found a tutor?

Use the following notation:

F= fail the course

P = passes the course

T = finds a tutor

Tc = does not find a tutor

Using the above notation, set up a PROBABILITY tree using the information in the paragraph above. Be

sure to label ALL the branches with both the notation for the probability AND the numerical value of

that probability

Then multiply the probabilities across the branches. Give both the numerical value AND the probabilities

they represent in notation.

Finally, use the definition of conditional probability and the results from your tree calculations to

calculate the chance Dana had found a tutor if she fails the final.

…

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