Math Quiz.- 3

MTH 165 Lund

Chapter 5 Take-home Quiz Covering 5.1, 5.2, 5.3, 5.4

NO TUTORING CENTER HELP.

No credit will be given without supporting work. A quiz consisting of multiple pages must be

stapled. Work must be legible and completed on a separate piece of paper.

All answers should include probability notation! Round all answers to 4 decimal places.

1. (1.5pts each) 500 people, all of whom drive approximately 10,000 miles per year, were classified according to age and the number of auto accidents each has had during the last three years:

Number of Accidents Age (in years)

Under 40 Over 40

0 150 100

1 90 60

More than 1 60 40

A person is selected at random from those 500.

a. What is the probability that the person selected is over 40 and has had more than 1 accident? b. What is the probability that the person selected is either over 40 or has had more than 1 accident (or

both)?

c. Find the probability that the person selected is over 40 given that he/she has had more than 1 accident. d. Suppose that the person selected is over 40. What is the probability that he/she has had more than 1

accident?

e. Find the probability that the person selected is over 40 given that he/she has had at most 1 accident. f. According to the data, are the following event independent: {Being over 40 years old} and {Getting in

more than 1 accident}? Justify your answer.

2. Suppose a 6-sided die is loaded where the probability of an outcome is

( ) ( ) ( ) ( ) ( ) ( ) where p is unknown.

a. (1pt) Find the value of p that would make this a valid probability model and then state the exact probability of rolling each number on the die.

b. (1pt)Which of the following events is more likely: or .

3. (1pt each) You reach into a bag that contains the following distribution of colored marbles: 6 green, 7 yellow, 3 purple. You will grab 2 marbles one at a time.

a. Find the probability that you first select a green and second a yellow marble. b. Find the probability that you select no green marbles in your two picks. c. Find the probability that you select exactly 1 purple marble and one non-purple marble. (Careful,

there are multiple cases to consider here)

4. (1pt each) A bank classifies borrowers as "high risk" or "low risk," and 20% of its loans are made to those in the "high risk" category. Five percent of all bank loans are in default. It is also known that if a

given loan is in default, there is 40% chance that it was issued to a high-risk borrower. Hint: since this

problem doesn’t have raw data, create a table or a Venn diagram first. I’ve started one for you without

the probabilities entered.

a. What is the probability that a randomly selected loan is in default and issued to a high-risk borrower? b. What is the probability that a loan will default, given that it is issued to a high-risk borrower? c. What is the probability that a randomly selected loan is either in default or issued to a high-risk

borrower, or both?

d. A loan is being issued to a borrower who is not high-risk. What is the probability that this loan will default?

5. (1pt each) Maxine goes to school 4 days a week. She can either arrive in time for class or be late. Her tardiness on any given day is independent of all other days. If the probability that Maxine is late on any

given day is 0.08…

a. …find the probability that she is in time for class for the first two days and tardy for the next two days.

b. …find the probability that she is late on at least one of the four days of the week.

High

Risk

Low

Risk

Default

Default C