Chapter 5: Probability

Question 1

PROBABILITY

Answer 1

The study of understanding and determining the outcomes of events yet to happen.
A measure of the likelihood of chance behavior.
Along-term prognosis.

Question 2

EXPERIMENT

Answer 2

In probability, any process with uncertain results that can be repeated.

Question 3

OUTCOME

Answer 3

One of the results of an experiment

Question 4

SAMPLE SPACE (“S”)

Answer 4

The collection of all outcomes from a probability experiment

Question 5

EVENT (“E”, “F”, etc.)

Answer 5

A subset of the sample space

Question 6

Intersection of 2 Events E and F

Answer 6

The collection of all outcomes in both E and F. Denoted E and F or E ∩ F):

Question 7

Disjoint (mutually exclusive) Events

Answer 7

Events are disjoint if they have NO OUTCOMES IN COMMON.

Question 8

Union of 2 Events E and F

Answer 8

The collection of all outcomes in either E or F or both. Denoted E or F or E ∪ F):

Question 9

Complement of an Event E

Answer 9

The collection of outcomes in the sample space NOT IN E. Denoted E^C

Question 10

Impossible Event

Answer 10

An event E such that the probability of E = 0.

Question 11

Sure Event

Answer 11

An event E such that the probability of E = 1.

Question 12

Unusual Event

Answer 12

Event: An event E such that the probability of E ≤ 0.05.

Question 13

THE FUNDAMENTAL RULES OF PROBABILITY

Answer 13

1. The probability of any event E, P(E), is a NUMBER that must be greater than or equal to 0 and less than or equal to 1. That is, 0 ≤ P(E) ≤ 1
2. If the sample space S = {e1, e2, …, en}, then P(e1) + P(e2) + … + P(en) = 1. That is, the sum of the probabilities of all the outcomes must equal 1. Another way to write this is that P(S) = 1.

Question 14

Classical Method of Computing Probabilities

Answer 14

Assumes equally likely outcomes; that is, all Outcomes are assumed to have the same probability of occurring.
So, if S is the sample space of this experiment,

             P(E) = N(E)/N(S)

where N(E) is the number of outcomes in E, and N(S) is the number of outcomes in the sample space.

Question 15

Marginal Probability (Unconditional Probability)

Answer 15

When an experiment involves more than one event, the probability of one of the events, irrespective of the presence of the other events. It is computed as the relative frequency of the event relative to the total population.

Question 16

Joint Probability of Two Events, E and F

Answer 16

The probability of the intersection of two events; namely P(E and F).

Question 17

Conditional Probability of Two Events

Answer 17

If E and F are any two events, then:

P(F / E) = ( 𝑷(𝑭 𝒂𝒏𝒅 𝑬))/(𝑷(𝑬)) = ( 𝑷(𝑬 𝒂𝒏𝒅 𝑭))/(𝑷(𝑬))

The expression P(F / E) is read “the probability of event F given event E”.

Question 18

General Multiplication Rule

Answer 18

The probability that two events E and F both occur is:

P(E and F) = P(E) * P(F|E)

Question 19

Independent Events, E and F

Answer 19

The occurrence of event E in a probability experiment does not affect the probability of event F (or vice versa).

Question 20

Computing Probabilities Using the Relative Frequency (Empirical) Method

Answer 20

For an event E of an experiment, we define the relative frequency of E as

( the number of times the event E was observed)/(the number of repetitions of the experiment)

We then define the P(E) to equal this relative frequency

Question 21

Computing Probabilities Using the Relative Frequency (Empirical) Method

Answer 21

For an event E of an experiment, we define the relative frequency of E as

( the number of times the event E was observed)/(the number of repetitions of the experiment)

We then define the P(E) to equal this relative frequency

Question 22

General Addition Rule for Joint Events

Answer 22

If E and F are disjoint (mutually exclusive) events, then

P(E pr F) = P(E) + P(F)

Question 23

Probability Model

Answer 23

A list of the possible outcomes of an experiment and each outcome’s probability. Must satisfy both fundamental rules of probabilities

Question 24

Probability Model

Answer 24

A list of the possible outcomes of an experiment and each outcome’s probability. Must satisfy both fundamental rules of probabilities, (0 ≤ P(E) ≤ 1) and
P(S) = 1.

Question 25

The Empty Event

Answer 25

p(E) = 0

Question 26

The Law of Large Numbers

Answer 26

As the number of repetitions of a probability experiment increases, the proportion (relative frequency) with which a certain outcome is observed gets closer to the classical probability of the outcome.

Question 27

Complement Rule

Answer 27

If E represents any event and E^C represents the complement of E, then: P(E) + P(E^C) = 1 - P(E^C)

Question 28

Multiplication Rule for Independent Events

Answer 28

If E and F are independent events, then

P(E and F) = P(E) * P(F)

Question 29

Simulation

Answer 29

A technique used to recreate a random event

Question 30

Contingency Table (Two-Way Table)

Answer 30

A table that relates two categories of data.

Question 31

Dependent Events, E and F

Answer 31

The occurrence of event E in a probability experiment affects the probability of event F (or vice versa).