MTH 165 Quiz 3 (3.1 & 3.2)
Name ________________________________________________
• DUE Tuesday May 30th by 11:59pm.
• Show sufficient work to justify each answer as demonstrated in the lecture videos.
Work should be presented in an organized and logical fashion. State all answers as
exact values.
• Write neatly and use proper notation throughout your work.
• You should be able to complete these problems in 25 minutes. If you need more time
you may not be ready to complete these problems in a timely fashion on the exam.
1. (2pts 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 TOTAL
0 160 90 250
1 80 70 150
More than 1 60 40 100
TOTAL 300 200 500
A person is selected at random from those 500.
a) What is the probability that a person selected is under 40?
b) What is the probability that the person selected is over 40 and has had more than 1 accident?
c) What is the probability that the person selected is either over 40 or has had more than 1 accident, or
both?
15
d) Find the probability that the person selected has had 0 accidents or has had more than 1 accident.
e) What is the probability that the person selected is both over 40 and has been in under 2 accidents?
f) What is the probability that the person selected is under 40 or has been in at least 1 accident?
2. Suppose a 6-sided die is weighted so that the probability of an outcome is proportional to the outcome.
That is,
( ) ( ) ( ) ( ) ( ) ( )1 2 2 3 3 4 4 5 5 6 6P p P p P p P p P p P p= = = = = =
(here p stands for a mystery number)
a. (1.5pts) Find the value of p that would make this a valid probability model and then state the exact (in
fraction form) probability of rolling each number on the die.
b. (1.5pts) Which of the following events is more likely: 6rolling a or 1 2rolling a or ? Use your
work from part (a) to justify your answer.