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What is the definition of probability?
The chance of likelihood of an event occurring

What is the sample space?
The set of all possible outcomes of an experiment or situation

How do you represent the sample space for a coin?
S = {Head, Tail}

How do you represent the sample space for a die?
S = {1, 2, 3, 4, 5, 6}

What are events?
 Collection of outcomes or sample points resulting from an experiment
 Example: Roll a die (experiment) and get a 3 (event A). A = {3}
 Example: Roll a die (experiment) and get a number > 3 (event B). B = {4, 5, 6}

What is the classical method of assigning properties?
 Assigning based on the assumption of equally likely outcomes
 All the same weight

How do you assign probabilities in terms of longrun relative frequency?
Assigning based on experimentation or historical values

How do you assign probabilities subjectively?
Asses based on judgement, experience, expertise, or intuition

What is the difference between probability and uncertainty?
 Probability means knowing the likelihood of something occuring
 Uncertainty means you can't even guess what the outcome or value will be

What are the limits of a probability value?
0 and 1

What must the sum of all probabilities in an experiment equal?
1

In the Classical Method, if an experiment has n possible outcomes, what is the probability of each?
1/n

What is the counting rule for multistep experiments?

For an experiment involving a coin flipped 3 times, how would you show that in probabilities?
(2)(2)(2) = 8 possible outcomes

How is factorial represented?

What is the equation for Counting Rule Combinations?

What is the equation for Counting Rules Permutations?

What happens when then number of permutations can repeat in counting rules?
 The number of permutations becomes exponential
 Example: Set a password with 8 characters, case sensitive, plus numbers
 Total options = 62
 Total draws = 8

What is the Relative Frequency Method of probabilities?
 Assigning probabilities based on historical data
 Things you noticed in the past

What is the Subjective Method of assigning probabilities?
When you assign based on some historical data and a degree of personal belief in what will occur.

What is the Complement of an Event?
 It's a probability event of all the sample points that WILL NOT occur in another event.
 S = {1,2,3,4,5,6}
 A = {3}
 A^{c} = {1,2,4,5,6}

What are the notations for a Complement of an Event?
 A^{c}
 A^{1}

What is the Complement of an Event equation?
P(A^{c}) = 1  P(A)

What is the Union of 2 Events?
 The event containing all sample points that are in A OR B OR Both
 OR
 A = {3,4,5,6} B = {2,3,4}
 = {2,3,4,5,6}

What is the notation for Union of 2 Events?
 A or B

What is the Intersection of 2 Events?
 The set of all sample points that are in both A AND B
 AND
 A = {3,4,5,6} B = {2,3,4 }
 {3,4}
 2/6

What is the notation for the Intersection of 2 Events?
 A and B
 junction

What is Addition Law?
It's used to compute the probability of the union of two events.

What is the Addition Law equation?

Which counting rule do you use when the order does NOT matter?
 Combinations
 NOT permutations

Rolling a die
A = {3,4,5,6}
B = (2,3,4}
What is ?
What is ?
 {3, 4}
 {2,3,4,5,6}

If rolling a die and {3,4}, what is ?
2/6 or 1/3

If rolling a die and {2,3,4,5,6}, what is P ?
5/6

What are mutually exclusive events?
 Have no sample points in common
 If one occurs, the other cannot occur

What is true if Events A and B are mutually exclusive?

What is the Addition Law equation of Events A and B if Events A and B are mutually exclusive?


What is Conditional Probability?
 The probability of an event A, given that the event B has occurred

What is the Conditional Probability equation?

What happens to the sample space in ?
Event A is restricted to the new sample space of B

P(A) = 2/3
P(B) = 1/2
What is ?
 2/3

 1/2

A = {3,4,5,6}
B = {2,3,4}
{3,4}
What is P(A)?
What is P(B)?
What is ?
 P(A) = 2/3
 P(B) = 1/2
 1/3

C = {1,2}
A = {3,4,5,6}
Are Events A and C mutually exclusive?
 Yes

What is the Multiplication Rule used for?
Compute the intersection between 2 events

What is the equation for the Multiplication Rule?

What is P(B)?

 0.16

Given a standard deck of cads, what is the probability of drawing a red card, given that it is a face card?

Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card?
 0.24

If P(A) is not changed or affected by the existence of event B, then A and B are what?
Independent events

P(AB) = P(A)
Are A and B independent events?
Yes

P(AB) = P(B)
Are A and B independent events?
 No
 P(BA) = P(B)  This would be independent

A = {3,4,5,6}
B = {2,3,4}
Determine if A and B independent using the Conditional Probability method.
 Independent
 P(A) = 2/3
 P(B) = 1/2
 P(AB) = 2/3 = P(A)
 P(BA) = 1/2 = P(B)

A = {3,4,5,6}
B = {2,3,4}
Determine if A and B are independent using the Multiplication rule.
 Yes
 P(A) = 2/3
 P(B) = 1/2

A and B are independent
P(A) = 0.2
P(B) = 0.7
What is
 0.14

A and B are independent
P(A) = 0.2
P(B) = 0.7
What is
 0.86

A and B are mutually exclusive
What is

P(A) = 0.3
P(B) = 0.5
Are A and B independent?
 Yes
  If independent

P(A) = 0.3
P(B) = 0.5
Are A and B mutually exclusive?
 No
  If mutually exclusive


In a probability matrix, what does the bottom right corner contain?
1.00 meaning 100%

