Question 1

An electronics firm manufactures three models of stereo receivers, two cassette decks, four speakers and three CD players. When the four types of components are sold together, they form a "system." How many different systems can the electronic firm offer?
A) 36
B) 18
C) 72
D) 144
E) None of the choices are correct

Accepted Answer

To find the total number of different systems, multiply the number of choices for each component: 3 stereo receivers × 2 cassette decks × 4 speakers × 3 CD players = 72 different systems.

Question 2

What does  equal?
A) 640
B) 36
C) 10
D) 120
E) None of the choices are correct

Accepted Answer

C

Question 3

A builder has agreed not to erect all "look alike" homes in a new subdivision. Five exterior designs are offered to potential homebuyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors. How many different ways are the exterior and interior plans offered to potential homebuyers?
A) 8
B) 10
C) 15
D) 30
E) None of the choices are correct

Accepted Answer

There are 5 exterior designs and 3 interior plans, so there are 5 * 3 = 15 different ways the exterior and interior plans can be offered to potential homebuyers.

Question 4

i. A probability is usually expressed as a decimal, such as 0.70 or 0.27, but it may be given as a fraction, such as 7/10 or 27/100.
Ii) The probability of 1 represents something that is certain to happen. 
iii. The probability of 0 represents something that cannot happen.
A) (i), (ii) and (iii) are all correct statements
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Accepted Answer

All three statements are correct: probabilities can be expressed as decimals or fractions, a probability of 1 means an event is certain, and a probability of 0 means an event cannot happen.

Question 5

i. The Cunard luxury liner, Queen Elizabeth 2, cannot be docked in Hong Kong and Bangkok at the same time. Events such as these that cannot occur simultaneously are said to be collectively exhaustive.
Ii) If there are 'm' ways of doing one thing and 'n' ways of doing another thing, the multiplication formula states that there are (m) • (n) ways of doing both.
Iii) A permutation is an arrangement of a set of objects in which order does not matter.
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) All statements are false

Accepted Answer

Statement (i) is incorrect because events that cannot occur simultaneously are called mutually exclusive, not collectively exhaustive. Statement (ii) is correct as it describes the multiplication principle. Statement (iii) is incorrect because a permutation is an arrangement where order does matter.

Question 6

The result of a particular experiment is called a(n)
A) observation.
B) conditional probability.
C) event.
D) outcome.
E) None of the choices are correct.

Accepted Answer

An outcome is the result of a single trial of an experiment.

Question 7

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.
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) All statements are false

Accepted Answer

The answer of i. A subjective probability can be assigned...

Question 8

Six basic colours are to be used in decorating a new condominium. They are to be applied to a unit in groups of four colours. One unit might have gold as the principal colour, blue as a complementary colour, red as the accent colour and touches of white. Another unit might have blue as the principal colour, white as the complimentary colour, gold as the accent colour and touches of red. If repetitions are permitted, how many different units can be decorated?
A) 7,825
B) 25
C) 125
D) 1,296
E) None of the choices are correct

Accepted Answer

Since repetitions are permitted, each of the four positions (principal, complementary, accent, touches) can be filled by any of the six colors. Therefore, the total number of combinations is 6^4 = 1,296.

Question 9

i. An illustration of an experiment is turning the ignition key of an automobile as it comes off the assembly line to determine whether or not the engine will start. 
ii. If there are 'm' ways of doing one thing and 'n' ways of doing another thing, the multiplication formula states that there are (m)-(n) ways of doing both.
Iii) A permutation is an arrangement of a set of objects in which there is an order from the first through the last.
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) All statements are false

Accepted Answer

(i) is an example of a test, not an experiment. (ii) is the multiplication principle, which is a correct statement. (iii) is the definition of a permutation, which is also a correct statement.

Question 10

The numbers 0 through 9 are to be used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?
A) 5,040
B) 620
C) 10,200
D) 120
E) None of the choices are correct

Accepted Answer

The number of different code groups can be calculated by finding the number of permutations of 4 digits selected from 10 digits (0-9) without repetition. This is given by 10P4 = 10! / (10-4)! = 10 x 9 x 8 x 7 = 5,040.

Question 11

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.)
A) 45
B) 50
C) 125
D) 14
E) None of the choices are correct

Accepted Answer

The number of games required is calculated using the combination formula for choosing 2 teams out of 10 to play a game, which is 10 choose 2: C(10, 2) = 45.

Question 12

i. The probability of an event, based on a classical approach, is defined as the number of favourable outcomes divided by the total number of possible outcomes.
Ii) If among several events only one can occur at a time, we refer to these events as being mutually exclusive events.
Iii) The probability of rolling a 3 or 2 on a single die is an example of conditional probability.
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) All statements are false

Accepted Answer

Statement (i) correctly defines the classical probability approach. Statement (ii) correctly describes mutually exclusive events. Statement (iii) is incorrect because rolling a 3 or 2 on a die is an example of simple probability, not conditional probability.

Question 13

Six basic colours are to be used in decorating a new condominium. They are to be applied to a unit in groups of four colours. One unit might have gold as the principal colour, blue as a complementary colour, red as the accent colour and touches of white. Another unit might have blue as the principal colour, white as the complimentary colour, gold as the accent colour and touches of red. If repetitions are not permitted, how many different units can be decorated?
A) 360
B) 25
C) 125
D) 1,296
E) None of the choices are correct

Accepted Answer

The number of ways to choose 4 colours out of 6 is given by the combination formula C(6,4) = 15. For each group of 4 colours, there are 4! = 24 ways to assign them as principal, complementary, accent, and touches. Therefore, the total number of different units is 15 * 24 = 360.

Question 14

A rug manufacturer has decided to use 7 compatible colours in her rugs. However, in weaving a rug, only 5 spindles can be used. In advertising, the rug manufacturer wants to indicate the number of different colour groupings for sale. How many colour groupings using the seven colours taken five at a time are there? (This assumes that 5 different colours will go into each rug, i.e., there are no repetitions of colour.)
A) 120
B) 2,520
C) 6,740
D) 36
E) None of the choices are correct

Accepted Answer

The answer of A rug manufacturer has decided to use...

Question 15

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?
A) 4
B) 24
C) 120
D) 37
E) None of the choices are correct

Accepted Answer

The number of ways to organize calls on four hospitals is the number of permutations of 4 items, which is 4! (4 factorial), equal to 24.

Question 16

i. A probability is usually expressed as a decimal, such as 0.70 or 0.27, but it may be given as a fraction, such as 7/10 or 27/100.
Ii) The closer a probability is to 0, the more likely that an event will not happen. 
iii. The closer the probability is to 1.00, the more likely an event will happen.
A) (i), (ii) and (iii) are all correct statements
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Accepted Answer

All three statements are correct. Probabilities can be expressed as decimals or fractions, and a probability closer to 0 indicates an event is less likely to happen, while a probability closer to 1 indicates an event is more likely to happen.

Question 17

When are two events mutually exclusive?
A) They overlap on a Venn diagram
B) If one event occurs, then the other cannot
C) Probability of one affects the probability of the other
D) Both (a) and (b)
E) None of the choices are correct

Accepted Answer

If one event occurs, then the other cannot

Question 18

You have the assignment of designing colour codes for different parts. Three colours are to be used on each part, but a combination of three colours used for one part cannot be rearranged and used to identify a different part. This means that if green, yellow and violet were used to identify a camshaft, yellow, violet and green (or any other combination of these three colours) could not be used to identify a pinion gear. If there are 35 combinations, how many colours were available?
A) 5
B) 7
C) 9
D) 11
E) None of the choices are correct

Accepted Answer

The number of combinations of 3 colors from n available colors is given by the combination formula C(n, 3) = n! / (3!(n-3)!). Setting this equal to 35, we solve for n: C(n, 3) = 35 => n(n-1)(n-2)/6 = 35. Solving this equation gives n = 7.

Question 19

i. A probability is usually expressed as a decimal, such as 0.70 or 0.27, but it may be given as a fraction, such as 7/10 or 27/100. 
ii. The closer a probability is to 0, the more likely that an event will happen.
Iii) The closer the probability is to 1.00, the more likely an event will not happen.
A) (i), (ii) and (iii) are all correct statements
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Accepted Answer

Statement (i) is correct as probabilities can be expressed as decimals or fractions. Statement (ii) is incorrect because the closer a probability is to 0, the less likely an event will happen. Statement (iii) is incorrect because the closer a probability is to 1, the more likely an event will happen.

Question 20

i. The Cunard luxury liner, Queen Elizabeth 2, cannot be docked in Hong Kong and Bangkok at the same time. Events such as these that cannot occur simultaneously are said to be collectively exhaustive.
Ii) If there are 'm' ways of doing one thing and 'n' ways of doing another thing, the multiplication formula states that there are (m)(n) ways of doing both.
Iii) A permutation is an arrangement of a set of objects in which there is an order from the first through the last.
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) All statements are false

Accepted Answer

Statement (i) is incorrect because events that cannot occur simultaneously are called mutually exclusive, not collectively exhaustive. Statements (ii) and (iii) are correct.

Quiz 4: A Survey of Probability Concepts

An electronics firm manufactures three models of stereo receivers, two cassette decks, four speakers and three CD players. When the four types of components are sold together, they form a "system." How many different systems can the electronic firm offer?

What does equal?

i. A probability is usually expressed as a decimal, such as 0.70 or 0.27, but it may be given as a fraction, such as 7/10 or 27/100. Ii) The probability of 1 represents something that is certain to happen. iii. The probability of 0 represents something that cannot happen.

The result of a particular experiment is called a(n)

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?

i. A probability is usually expressed as a decimal, such as 0.70 or 0.27, but it may be given as a fraction, such as 7/10 or 27/100. Ii) The closer a probability is to 0, the more likely that an event will not happen. iii. The closer the probability is to 1.00, the more likely an event will happen.

When are two events mutually exclusive?

i. A probability is usually expressed as a decimal, such as 0.70 or 0.27, but it may be given as a fraction, such as 7/10 or 27/100. ii. The closer a probability is to 0, the more likely that an event will happen. Iii) The closer the probability is to 1.00, the more likely an event will not happen.