Question 1

The following distribution table represents preferences for two types of cereals by 2000 boys and girls.  Determine the probability that the person is a boy, given that the person likes Fruity Cereal.

Accepted Answer

A)  500/1,000 
B)  500/2,000 
C)  1,200/2,000 
D)  500/1,200

Question 2

If two events are independent, then their joint probability is

Accepted Answer

A)  computed with the special rule of addition 
B)  computed with the special rule of multiplication 
C)  computed with the general rule of multiplication 
D)  computed with Bayes theorem

Question 3

i. A subjective probability can be assigned to an event by an individual based on the individual's knowledge about the event. ii. The probability that you would assign to the likelihood that the Hamilton Tiger Cats will be in the Grey Cup this season must be between 0 and 10.
iii. A probability is a number from -1 to +1 inclusive that measures one's belief that an event resulting from an experiment will occur.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and, (ii) are correct statements but not (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and, (iii) are correct statements but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 4

Information on the 30 Major League Baseball teams for the 2003 season has been summarized based on game attendance. What is the probability that if a team is selected at random, it had a winning season or attendance of more than 3.0 million?

Accepted Answer

A)  18/30 
B)  19/30 
C)  13/30 
D)  9/30 
E)  12/30

Question 5

Considering the chart below, what is the probability that if you select one person at random that they have committed a violent crime and were over 40 years of age?

Accepted Answer

A)  36.7% 
B)  5.6% 
C)  18.1% 
D)  9.3%

Question 6

When applying the special rule of addition for mutually exclusive events, the joint probability is:

Accepted Answer

A)  1 
B)  5 
C)  0 
D)  0.25 
E)  unknown

Question 7

A study by Tourism Ontario revealed that 50% of the vacationers going to Toronto visit the CN Tower, 40% visit SkyDome and 35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?

Accepted Answer

A)  0.95 
B)  0.35 
C)  0.55 
D)  0.05

Question 8

Consideration is being given to forming a Super Ten Basketball Conference. The top 10 university basketball teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. How many games would the conference commissioner have to schedule each year? (Remember, McMaster versus Alberta is the same as Alberta versus McMaster.)

Accepted Answer

A)  45 
B)  50 
C)  125 
D)  14

Question 9

The following distribution table represents preferences for two types of cereals by 2000 boys and girls.  Find the probability that an individual selected at random will be a boy and prefer Fruity cereal.

Accepted Answer

A)  500/1,000 
B)  500/2,000 
C)  1,200/2,000 
D)  500/1,200

Question 10

A study was done of the 377 vehicles parked in the college parking lot last Friday. The results follow.  What is the probability of finding a car that is not white?

Accepted Answer

A)  60/377 
B)  317/377 
C)  47/60 
D)  361/377

Question 11

Each salesperson in a large department store chain is rated with respect to sales potential for advancement. These traits for the 500 salespeople were cross-classified into the following table:  What is the probability that the selected salesperson has below average sales ability or has a fair potential for advancement?

Accepted Answer

A)  16/500 
B)  16/154 
C)  300/500 
D)  188/500 
E)  204/500

Question 12

A study was done of the 377 vehicles parked in the college parking lot last Friday. The results follow.  What is the probability of finding a red sports car?

Accepted Answer

A)  15/47 
B)  15/121 
C)  15/377 
D)  153/377

Question 13

A sales representative calls on four hospitals in York Region. It is immaterial what order he calls on them. How many ways can he organize his calls?

Accepted Answer

A)  4 
B)  24 
C)  120 
D)  37

Question 14

Which approach to probability is exemplified by the following formula?

Accepted Answer

A)  Classical approach 
B)  Empirical approach 
C)  Subjective approach

Question 15

i. An experiment is an activity that is either observed or measured. ii. If an experiment, such as a die-tossing experiment, has a set of events that includes every possible outcome, the set of events is called collectively exhaustive.
iii. The combination formula is: n!/(n - r)!

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and, (ii) are correct statements but not (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and, (iii) are correct statements but not (i). 
E)  (i), (ii) and (iii) are all false statements.

Question 16

There are two letters C and D. If repetitions such as CC are permitted, how many permutations are possible?

Accepted Answer

A)  1 
B)  0 
C)  4 
D)  8

Question 17

Considering the chart below, what is the probability that if you select one person at random that they have committed a violent crime, given that they were between 20 and 40 years of age?

Accepted Answer

A)  54.67% 
B)  56.23% 
C)  50.00% 
D)  18.0%

Question 18

A survey of 500 top Canadian companies reported what the companies' hiring outlook was for the next 18 months as well as the general company outlook for the economy over the same period of time.  Given that a randomly selected company has a favourable forecast, what is the probability that it plans to cut jobs during the next 18 months?

Accepted Answer

A)  25/500 
B)  25/175 
C)  125/175 
D)  175/500

Question 19

What does  equal?

Accepted Answer

A)  640 
B)  36 
C)  10 
D)  120

Question 20

When an experiment is conducted "without replacement",

Accepted Answer

A)  events are independent 
B)  events are equally likely 
C)  the experiment can be illustrated with a Venn Diagram 
D)  the probability of two or more events is computed as a joint probability

Exam 4: A Survey of Probability Concepts

The following distribution table represents preferences for two types of cereals by 2000 boys and girls. Determine the probability that the person is a boy, given that the person likes Fruity Cereal.

If two events are independent, then their joint probability is

Information on the 30 Major League Baseball teams for the 2003 season has been summarized based on game attendance. What is the probability that if a team is selected at random, it had a winning season or attendance of more than 3.0 million?

Considering the chart below, what is the probability that if you select one person at random that they have committed a violent crime and were over 40 years of age?

When applying the special rule of addition for mutually exclusive events, the joint probability is:

A study by Tourism Ontario revealed that 50% of the vacationers going to Toronto visit the CN Tower, 40% visit SkyDome and 35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?

The following distribution table represents preferences for two types of cereals by 2000 boys and girls. Find the probability that an individual selected at random will be a boy and prefer Fruity cereal.

A study was done of the 377 vehicles parked in the college parking lot last Friday. The results follow. What is the probability of finding a car that is not white?

A study was done of the 377 vehicles parked in the college parking lot last Friday. The results follow. What is the probability of finding a red sports car?

A sales representative calls on four hospitals in York Region. It is immaterial what order he calls on them. How many ways can he organize his calls?

Which approach to probability is exemplified by the following formula?

i. An experiment is an activity that is either observed or measured. ii. If an experiment, such as a die-tossing experiment, has a set of events that includes every possible outcome, the set of events is called collectively exhaustive. iii. The combination formula is: n!/(n - r) !

There are two letters C and D. If repetitions such as CC are permitted, how many permutations are possible?

Considering the chart below, what is the probability that if you select one person at random that they have committed a violent crime, given that they were between 20 and 40 years of age?

What does equal?

When an experiment is conducted "without replacement",