OpenStax - Ch. 3 Probability Topics

Question 1

Conditional Probability

Answer 1

the likelihood that an event will occur given that another event has already occurred.

Question 2

contingency table

Answer 2

the method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; the table provides an easy way to calculate conditional probabilitie.

Question 3

Dependent Events

Answer 3

If two events are NOT independent, then we say that they are dependent.

Question 4

Equally Likely

Answer 4

Each outcome of an experiment has the same probability.

Question 5

Event

Answer 5

a subset of the set of all outcomes of an experiment; the set of all outcomes of an experiment is called a sample space and is usually denoted by S.

An event is an arbitrary subset in S. It can contain one outcome, two outcomes, no outcomes (empty subset), the entire sample space, and the like. Standard notations for events are capital letters such as A, B, C, and so on.

Question 6

Experiment

Answer 6

a planned activity carried out under controlled conditions.

Question 7

Independent Events

Answer 7

The occurrence of one event has no effect on the probability of the occurrence of another event.

Events A and B are independent if one of the following is true:

P(A|B) = P(A)

P(B|A) = P(B)

P(A AND B) = P(A)P(B)

Question 8

Mutually Exclusive

Answer 8

Two events are mutually exclusive if the probability that they both happen at the same time is zero. If events A and B are mutually exclusive, then P(A AND B) = 0.

Question 9

Outcome

Answer 9

a particular result of an experiment.

Question 10

Probability

Answer 10

a number between zero and one, inclusive, that gives the likelihood that a specific event will occur; the foundation of statistics is given by the following 3 axioms (by A.N. Kolmogorov, 1930’s): Let S denote the sample space and A and B are two events in S.

Then:

0 ≤ P(A) ≤ 1

If A and B are any two mutually exclusive events, then P(A OR B) = P(A) + P(B).

P(S) = 1

Question 11

Sample Space

Answer 11

the set of all possible outcomes of an experiment.

Question 12

Sampling with Replacement

Answer 12

If each member of a population is replaced after it is picked, then that member has the possibility of being chosen more than once.

Question 13

Sampling without Replacement

Answer 13

When sampling is done without replacement, each member of a population may be chosen only once.

Question 14

The AND Event

Answer 14

An outcome is in the event A AND B if the outcome is in both A AND B at the same time.

Question 15

The Complement Event

Answer 15

The complement of event A consists of all outcomes that are NOT in A.

Question 16

The Conditional Probability of A GIVEN B

Answer 16

P(A|B) is the probability that event A will occur given that the event B has already occurred.

Question 17

The Conditional Probability of One Event Given Another Event

Answer 17

P(A|B) is the probability that event A will occur given that the event B has already occurred.

Question 18

The Or Event

Answer 18

An outcome is in the event A OR B if the outcome is in A or is in B or is in both A and B.

Question 19

The OR of Two Events

Answer 19

An outcome is in the event A OR B if the outcome is in A, is in B, or is in both A and B.

Question 20

Tree Diagram

Answer 20

the useful visual representation of a sample space and events in the form of a “tree” with branches marked by possible outcomes together with associated probabilities (frequencies, relative frequencies).

Question 21

Venn Diagram

Answer 21

the visual representation of a sample space and events in the form of circles or ovals showing their intersections.