Business Statistics Ch. 4

Front 1

probability definition

Back 1

a numerical value ranging from 0 to 1;
indicates the chance of a specific event occurring:
-if there is no chance of the event occurring, the probability is 0;
-if the event is absolutely going to occur, the probability is 1

Front 2

experiment definition

Back 2

the process of measuring or observing an activity for the purpose of collecting data;
an example is rolling a single 6 sided die

Front 3

sample space definition

Back 3

all the possible outcomes of an experiment;
the sample space for our single-die experiment is {1, 2, 3, 4, 5, 6}
-numbers in braces signal they represent sample space

Front 4

event definition

Back 4

1 or more outcomes of an experiment;
the outcome(s) is a subset of the sample space;
an example of an event is rolling a pair with two dice

Front 5

simple event definition

Back 5

an event with a single outcome in its most basic form that cannot be simplified;
an example of a simple event is rolling a 5 with a single die

Front 6

methods of assigning probability

Back 6

classical, empirical, and subjective

Front 7

classical probability forumula

Back 7

# of possible outcomes that constitute event A
P(A) = ----------------------------------------------------------------
total number of possible outcomes in the sample space

where: P(A) = the probability that event A will occur

Front 8

empirical probability definition

Back 8

involves conducting an experiment to OBSERVE the frequency of which an event occurs

Front 9

formula for empirical probability

Back 9

frequency in which event A occurs
P(A) = ---------------------------------------------------------
total number of observations

Front 10

law of large numbers

Back 10

states that when an experiment is conducted a large number of times, the empirical probabilities of the process will converge to the classical probabilities;
example: flip a coin a large number of times, the observed number of heads would be very close to 50%

Front 11

subjective probability definition

Back 11

used when classical and empirical probabilities aren't available;
instead use experience or intuition to estimate the probabilities;

Front 12

basic properties of a probability

Back 12

rule 1: if P(A) = 1, then with certainty, event A must occur
rule 2: if P(A) = 0, then with certainty, event A will not occur
rule 3: the probability of any event must range from 0 to 1
rule 4: the sum of all the probabilities for the simple events in the sample space must be equal to 1
rule 5: the complement to event A is defined as all of the outcomes in the sample space that are not part of event A; the complement is denoted as A'

Front 13

formula for the complement rule

Back 13

P(A) + P(A') = 1
or
P(A) = 1 - P(A')

Front 14

probability rules for more than one event

Back 14

many situations involve 2 or more events that intersect with one another;
a contingency table can be used to show the number of occurrences of events that are classified according to 2 categorical variables

Front 15

marginal probability is another term used for...

Back 15

simple probability

Front 16

intersection

Back 16

represents the number of instances in which events A and B occur at the same time

Front 17

joint probability definition

Back 17

probability of the intersection of 2 events

Front 18

P(Ace∩Red)

Intersection of events

Back 18

also denoted as P(Ace and Red)

Front 19

The union of events A and B represents...

Back 19

the number of instances where EITHER event A or B occur OR both events occur together

Front 20

P(Ace∪Red)

Union of events

Back 20

is also denoted as P(ace or red)

Front 21

The addition rule for probabilities...

Back 21

is used to calculate the probability of the union of events;
the probability that event A, or event B, or both events will occur;
the 2 events are considered to be MUTUALLY EXCLUSIVE if they can't occur at the same time during the experiment

Front 22

Mutually exclusive forumula

Back 22

P(A or B) = P(A) + P(B)

Front 23

If events A and B are NOT mutually exclusive formula

Back 23

P(A or B) = P(A) +P(B) - P(A and B)

Front 24

Conditional probability definition

Back 24

the probability of event A occurring, given the condition that event B has occurred;
AKA posterior probability

Front 25

formula for calculating conditional probability

Back 25

Front 26

Independent events definition

Back 26

2 events are considered independent of one another if the occurrence of one event has no impact on the occurrence of the other event

Front 27

Dependent event definition

Back 27

if the occurrence of one event affects the occurrence of another event, the events are considered dependent

Front 28

formula for determining if events A and B are independent

Back 28

Front 29

If P(A|B) ≠ P(A) then...

Back 29

events A and B are NOT independent

Front 30

The multiplication rule...

Back 30

is used to determine the probability of the intersection (joint probability) of 2 events occurring, or P(A and B)

Front 31

Multiplication rule formula for dependent events

Back 31

Front 32

Multiplication rule formula for dependent events (other way)

Back 32

Front 33

formula for the multiplication rule for 2 independent events

Back 33

Front 34

convert table frequencies into probabilities by...

Back 34

dividing each number in the table by the total number of observations

Front 35

Decision trees definition

Back 35

used to display marginal and joint probabilities from a contingency table