Question 1

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

Accepted Answer

The special rule of addition for mutually exclusive events states that if two events are mutually exclusive, then the probability of either event occurring is the sum of their individual probabilities. Since mutually exclusive events cannot occur at the same time, their joint probability is always zero. Therefore, the answer is C, 0.

Question 2

Which approach to probability assumes that events are equally likely?

Accepted Answer

The classical approach to probability assumes that events are equally likely. It is based on counting the number of possible outcomes that lead to a particular event and dividing that number by the total number of possible outcomes.

Question 3

When an experiment is conducted "without replacement," ________.

Accepted Answer

When an experiment is conducted "without replacement," events are dependent. This means that the outcome of one event affects the outcome of the next event.

Question 4

A graphical method used to calculate joint and conditional probabilities is ________.

Accepted Answer

A tree diagram is a graphical method commonly used to calculate joint and conditional probabilities. It allows users to see the different possible outcomes and the probabilities associated with each outcome. Venn diagrams are not typically used for this purpose and histograms are used to display distributions of data, rather than probabilities. Inferential statistics are used for hypothesis testing and making inferences about a population based on sample data.

Question 5

The first card selected from a standard 52-card deck was a king. If it is returned to the deck,what is the probability that a king will be drawn on the second selection?

Accepted Answer

Once the king is returned to the deck, there are 52 cards in the deck again, with 4 kings remaining. Therefore, the probability of selecting a king on the second draw is 4/52 or simplified 1/13.

Question 6

When are two experimental outcomes mutually exclusive?

Accepted Answer

Two experimental outcomes are mutually exclusive if they cannot both occur at the same time, meaning if one occurs, then the other cannot occur. This is the definition of mutually exclusive events.

Question 7

Six basic colors are used in decorating a new condominium. They are applied to a unit in groups of four colors. One unit might have gold as the principal color,blue as a complementary color,red as the accent color,and touches of white. Another unit might have blue as the principal color,white as the complementary color,gold as the accent color,and touches of red. If repetitions are permitted,how many different units can be decorated?

Accepted Answer

There are 6 options for the principal color, 5 remaining options for the complementary color, 4 options for the accent color, and 3 options for the last color. Thus, the number of possible combinations for one unit is:
6 x 5 x 4 x 3 = 360
Since repetitions are permitted, each of these 360 combinations can be used for any of the 4 color slots. Thus, the total number of different units that can be decorated is:
360^4 = 1,296. Therefore, option D is the correct answer.

Question 8

A rug manufacturer has decided to use seven compatible colors in her rugs. However,in weaving a rug,only five spindles can be used. In advertising,the rug manufacturer wants to indicate the number of different color groupings for sale. How many color groupings using the seven colors taken five at a time are there? (This assumes that five different colors will go into each rug-in other words,there are no repetitions of color.)

Accepted Answer

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

Question 9

A developer of a new subdivision wants to build homes that are all different. There are three different interior plans that can be combined with any of five different home exteriors. How many different homes can be built?

Accepted Answer

The number of different homes that can be built is found by multiplying the number of interior plans by the number of exterior plans, which is 3 * 5 = 15.

Question 10

The probability of two or more events occurring concurrently is called a(n)________.

Accepted Answer

Joint probability refers to the probability of two or more events occurring at the same time. Conditional probability refers to the probability of an event occurring given that another event has already occurred. Empirical probability is based on actual observations or experiments. A tree diagram is a diagram used to show all possible outcomes of an event or series of events. So, the best choice is C, joint probability.

Question 11

Probabilities are important information when ________.

Accepted Answer

Probabilities are a key component in inferential statistics, which involves making inferences or predictions about a population based on a sample.

Question 12

If two events are independent,then their joint probability is computed with ________.

Accepted Answer

When two events are independent, the joint probability is computed using the special rule of multiplication, which states that the probability of both events occurring is equal to the product of their individual probabilities. This rule is given by P(A and B) = P(A) * P(B). Therefore, the correct choice is B - the special rule of multiplication.

Question 13

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

Accepted Answer

The term "outcome" refers to the result of a particular experiment, so option D is the best choice. Option A refers to simply observing something, option B refers to the probability of a particular outcome given a condition, and option C refers to a specific set of outcomes.

Question 14

You are assigned to design color codes for different parts. Three colors are used to code on each part. Once a combination of three colors is used-such as green,yellow,and red-these three colors cannot be rearranged to use as a code for another part. If there are 35 combinations,how many colors are available?

Accepted Answer

Since there are 35 combinations and each combination requires three distinct colors, the total number of available colors can be calculated as 35 divided by the number of unique combinations that can be formed with three colors. This number is equal to 35 divided by the total number of combinations of 3 colors chosen from the total number of colors available. Using the formula for combinations (n choose r) = n!/r!(n-r)!, we can calculate that the total number of color choices must be a whole number greater than or equal to 7 and less than 8 (i.e., 35 / (n choose 3) = a whole number). The only whole number in this range that satisfies this condition is 7, so the answer is B, 7.

Question 15

The probability of a particular event occurring,given that another event has occurred,is known as a(n)________.

Accepted Answer

The given definition matches the concept of conditional probability. Therefore, option A is the correct choice. Empirical probability is based on observed frequencies and data, joint probability refers to the probability of two events occurring together, and a tree diagram is a graphical representation of possible outcomes of an event.

Question 16

The ABCD football association is considering a Super Ten Football Conference. The top 10 football 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,Oklahoma versus Michigan is the same as Michigan versus Oklahoma.)

Accepted Answer

This is a combination problem where you need to find how many games can be formed from 10 teams where the order does not matter (since Team A vs Team B is the same as Team B vs Team A). The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of items (teams), and k is the number of items to choose (2 for a game). So, C(10, 2) = 10! / [2!(10-2)!] = 45 games.

Question 17

The first card selected from a standard 52-card deck was a king. If it is NOT returned to the deck,what is the probability that a king will be drawn on the second selection?

Accepted Answer

Since one king has been removed, there are now 3 kings left out of the remaining 51 cards, making the probability 3/51 or 0.0588.

Question 18

An experiment may have ________.

Accepted Answer

An experiment can have one or more outcomes. For example, rolling a dice can have six possible outcomes (1, 2, 3, 4, 5, or 6), while flipping a coin has only two possible outcomes (heads or tails). Therefore, option C is the best choice.

Question 19

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows:  What is the probability that the first person selected is classified as a maintenance employee?

Accepted Answer

The probability that the first person selected is classified as a maintenance employee is equal to the number of maintenance employees divided by the total number of employees. From the information given, there are 20 maintenance employees out of a total of 800 employees:
P(maintenance) = 20/800 = 0.025, or 2.5%. Therefore, the answer is C.

Question 20

When an event's probability depends on the occurrence of another event,the probability is a(n)________.

Accepted Answer

Conditional probability is the probability of an event occurring given that another event has occurred. The occurrence of the second event affects the probability of the first event. Therefore, when the probability of an event depends on the occurrence of another event, it is known as the conditional probability.

Quiz 5: A Survey of Probability Concepts

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

Which approach to probability assumes that events are equally likely?

When an experiment is conducted "without replacement," ________.

A graphical method used to calculate joint and conditional probabilities is ________.

The first card selected from a standard 52-card deck was a king. If it is returned to the deck,what is the probability that a king will be drawn on the second selection?

When are two experimental outcomes mutually exclusive?

A developer of a new subdivision wants to build homes that are all different. There are three different interior plans that can be combined with any of five different home exteriors. How many different homes can be built?

The probability of two or more events occurring concurrently is called a(n) ________.

Probabilities are important information when ________.

If two events are independent,then their joint probability is computed with ________.

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

The probability of a particular event occurring,given that another event has occurred,is known as a(n) ________.

The first card selected from a standard 52-card deck was a king. If it is NOT returned to the deck,what is the probability that a king will be drawn on the second selection?

An experiment may have ________.

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows: What is the probability that the first person selected is classified as a maintenance employee?

When an event's probability depends on the occurrence of another event,the probability is a(n) ________.