Module 7, Probability

Question 1

Venn diagram

Answer 1

A type of chart that illustrates how distinct sets, topics, or objects relate to one another. Uses circles to represent events.

Question 2

complement

Answer 2

An event that is the opposite of another event. The complement of heads when flipping coins is tails. The probabilities of an event and its complement always sum to 1.

Question 3

Experiement

Answer 3

A procedure that can be done repeatedly which has a well defined set of outcomes.

Question 4

dependent events

Answer 4

Two events for which the occurrence of the first affects the probability of the second.

Question 5

relative frequency

Answer 5

A way to approximate a probability by taking the number of times an event occurs divided by the total number of trials.

Question 6

the law of large numbers

Answer 6

As the number of trials increases the empirical probability converges on the theoretical probability, that is the estimate of the true probability becomes more accurate.

Question 7

event

Answer 7

An outcome, or set of outcomes, whose chance of occurrence can be represented with a probability.

Question 8

sample size

Answer 8

The number of different outcomes for an experiment.

Question 9

tree diagram

Answer 9

A diagram that records all the events in a sample space by attaching each new set of events to each branch of the earlier events. The number of outermost branches gives the sample size.

Question 10

random experiment

Answer 10

Experiment in which the outcome is not known ahead of time and in which results do not affect future outcomes.

Question 11

conditional probability

Answer 11

A probability that depends on the occurrence of an earlier event.

Question 12

law of total probability

Answer 12

A fundamental principle of probability which states that the product of all branches of a probability tree, added together equals 1.

Question 13

probability

Answer 13

The chance of an event occurring.

Question 14

independent events

Answer 14

Events, where the occurrence of one does not affect the probability that the other event(s) will occur.

Question 15

probability tree

Answer 15

A tree diagram in which the branches record the probability of the next event and the nodes record the events.

Question 16

union

Answer 16

The union of A and B will have all elements in A, all elements in B, and all elements in both. You can think of a union as ‘A or B,’ since it contains an element if it is in A or in B. The union of many sets will have an element if it appears in at least one set.

Question 17

intersection

Answer 17

The intersection of A and B will have all elements that are in both A and B. You can think of an intersection as ‘A and B,’ since it contains an element if it is in A and in B. The intersection of many sets will have an element if it appears in all of the sets..

Question 18

frequency table

Answer 18

A table which records the frequency of instances in different categories. It can be used to determine if the categories are dependent or independent.

Question 19

sample space

Answer 19

The entire set of outcomes for a trial or experiment.

Question 20

fair

Answer 20

An experiment in which all outcomes are equally likely.

Question 21

theoretical probability

Answer 21

Also called the Actual, Exact, or Classical Probability, it is computed by dividing the number of outcomes where the desired event occurs by the total number of outcomes. Note that the outcomes must be equally likely.

Question 22

empirical probability

Answer 22

An estimation of probability derived from recording data about what has happened during a series of experiments.

Question 23

population

Answer 23

An entire pool from which a sample is drawn.

Question 24

disjoint

Answer 24

Two events which cannot both occur at the same time.

Question 25

multiplication rule for independent events

Answer 25

If two events are independent, then P(A and B) = P(A) x P(B).

Question 26

sample

Answer 26

The small quantity of data gathered about a population that will represent the population as a whole.