FORMULAS TO MEMORIZE PROBABILITY

Question 1

some process that occurs with well defined outcomes

Answer 1

experiment

Question 2

a result from a single trial of the experiment

Answer 2

outcome

Question 3

a collection of one or more outcomes

Answer 3

event

Question 4

a collection of all the outcomes of an experiment

Answer 4

sample space

Question 5

“expected” probability based upon knowledge of the situation, such as the number of outcomes

Answer 5

theoretical probability

Question 6

probability “estimate” based upon how often the event occured after collecting data from an experiment in a large number of trials

Answer 6

Empirical (experimental) probability

Question 7

V = or/union
N= and/intersection

Question 8

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

Answer 8

Probability Addition Rule

Question 9

The two events have no outcomes in common (equal ZERO)
P (A and B) must be equal to 0
P (A or B) = P(A) + P(B)

Answer 9

Mutually Exclusive Events

Question 10

Probability that event A occurs given that event B has already occured
“Probability of A given B”
P (A/B) = P(A and B)/P(B)

Answer 10

Conditional Probability

Question 11

The probability that one event occurs in no way affects the probability of the other event occurring
ex. rolling a die and flipping a coin

Answer 11

Independent Events

Question 12

The probability of one event occurring influences the likelihood of the other event
ex. Drawing a heart from a deck of cards, then drawing another heart from the deck

Answer 12

Dependent Events

Question 13

Events A and B are independent if
P(A) = P(A/B)
OR
P(A) x P(B) = P (A and B)

Answer 13

Testing for Independence
*one may be easier over another depending on what information is offered

Question 14

if an event has more than one stage to it, then a tree diagram can be drawn to list ALL the possible outcomes

Answer 14

Tree Diagrams/Sample Spaces

Question 15

P (A THEN B) = P(A) x P(B)

Answer 15

Multiplication Rule for Multi Stage Events

Question 16

If an object is replaced, and the probability of the second event does not change, then these events are independent

Answer 16

With replacement

Question 17

If an object is not replaced, and the probability of the second event changes, the denominator will ALWAYS be one less, the numerator is sometimes changed as well, thus, these events are dependent

Answer 17

Without replacement

Question 18

P(E) = n(E)/n(S)
n(E)= # of outcomes that fall into event E
n(S)= # of outcomes that fall into the sample space

Answer 18

Probability of an event E occurring

Question 19

0 (impossible) < P(event) < 1 (certain event)

Answer 19

range of probability

Question 20

P(Event) + P(NOT event) = 1

Answer 20

complement

Question 21

visualizes and keeps track of all possible outcomes in a sample space (union, intersection)

Answer 21

Venn diagrams

Question 22

P(neither) = 1 - P(at least one thing/policy)

Answer 22

chances of neither (opposite of or)

Question 23

2, 3, 5, 7, 11, 13, 17, 19, 23

Answer 23

Prime numbers

Question 24

the probability of an impossible event is 0 and the probability of a certain event 1

Answer 24

therefore the range of probability is 0 < P(E) <1
– –

Question 25

P(E) = P(not E) = 1
(aka complement)

Question 26

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

Answer 26

probability addition rule

Question 27

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

Answer 27

For mutually exclusive events (events with no outcomes in common)

Question 28

P(A|B) = n(A and B)/n(B) or P(A and B)/p(B)

Answer 28

Conditional Probability

Question 29

If the probability that one event occurs in no way affects the probability of the other event occurring

Answer 29

the events are independent

Question 30

If the probability of one event occurring influences the likelihood of the other event

Answer 30

the events are dependent

Question 31

Tests for Independence:
Events A and B are independent if:
1) P(A) = P(A|B)
2) P(A) x P(B) = P (A and B)

Question 32

Multiplication Rule for multi-stage events P(A then B)= P(A) x P(B)

Question 33

probability with replacement
if an object is replaced, the probability of the second event does not change

Question 34

probability without replacement, if an object is not replaced, the probability of the second event will change (the denominator will always be one less and the numerator may be changed)