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honestkyle
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What is the definition of probability?
The chance of likelihood of an event occurring
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What is the sample space?
The set of all possible outcomes of an experiment or situation
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How do you represent the sample space for a coin?
S = {Head, Tail}
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How do you represent the sample space for a die?
S = {1, 2, 3, 4, 5, 6}
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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}
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What is the classical method of assigning properties?
- Assigning based on the assumption of equally likely outcomes
- All the same weight
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How do you assign probabilities in terms of long-run relative frequency?
Assigning based on experimentation or historical values
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How do you assign probabilities subjectively?
Asses based on judgement, experience, expertise, or intuition
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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
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What are the limits of a probability value?
0 and 1
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What must the sum of all probabilities in an experiment equal?
1
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In the Classical Method, if an experiment has n possible outcomes, what is the probability of each?
1/n
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What is the counting rule for multi-step experiments?
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For an experiment involving a coin flipped 3 times, how would you show that in probabilities?
(2)(2)(2) = 8 possible outcomes
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How is factorial represented?
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What is the equation for Counting Rule Combinations?
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What is the equation for Counting Rules Permutations?
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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
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What is the Relative Frequency Method of probabilities?
- Assigning probabilities based on historical data
- Things you noticed in the past
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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.
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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}
- Ac = {1,2,4,5,6}
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What are the notations for a Complement of an Event?
- AcA1
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What is the Complement of an Event equation?
P(Ac) = 1 - P(A)
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What is the Union of 2 Events?
- The event containing all sample points that are in A OR B OR Both
- ORA = {3,4,5,6} B = {2,3,4}
 = {2,3,4,5,6}
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What is the notation for Union of 2 Events?
- A or B
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What is the Intersection of 2 Events?
- The set of all sample points that are in both A AND B
- ANDA = {3,4,5,6} B = {2,3,4 }
 {3,4}  2/6
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What is the notation for the Intersection of 2 Events?
 - A and B
- junction
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What is Addition Law?
It's used to compute the probability of the union of two events.
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What is the Addition Law equation?
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Which counting rule do you use when the order does NOT matter?
- Combinations
- NOT permutations
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Rolling a die
A = {3,4,5,6}
B = (2,3,4}
What is ?
What is ?
- {3, 4}
 {2,3,4,5,6}
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If rolling a die and {3,4}, what is  ?
2/6 or 1/3
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If rolling a die and {2,3,4,5,6}, what is P  ?
5/6
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What are mutually exclusive events?
- Have no sample points in common
- If one occurs, the other cannot occur
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What is true if Events A and B are mutually exclusive?
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What is the Addition Law equation of Events A and B if Events A and B are mutually exclusive?
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What is Conditional Probability?
- The probability of an event A, given that the event B has occurred
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What is the Conditional Probability equation?
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What happens to the sample space in ?
Event A is restricted to the new sample space of B
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P(A) = 2/3
P(B) = 1/2
What is ?
- 2/3
 
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- 1/2
 
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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
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C = {1,2}
A = {3,4,5,6}
Are Events A and C mutually exclusive?
- Yes
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What is the Multiplication Rule used for?
Compute the intersection between 2 events
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What is the equation for the Multiplication Rule?
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What is P(B)?
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- 0.16
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Given a standard deck of cads, what is the probability of drawing a red card, given that it is a face card?
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Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card?
- 0.24
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If P(A) is not changed or affected by the existence of event B, then A and B are what?
Independent events
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P(A|B) = P(A)
Are A and B independent events?
Yes
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P(A|B) = P(B)
Are A and B independent events?
- No
- P(B|A) = P(B) - This would be independent
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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(A|B) = 2/3 = P(A)
- P(B|A) = 1/2 = P(B)
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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
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A and B are independent
P(A) = 0.2
P(B) = 0.7
What is 
- 0.14
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A and B are independent
P(A) = 0.2
P(B) = 0.7
What is 
- 0.86
 
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A and B are mutually exclusive
What is 
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P(A) = 0.3
P(B) = 0.5
Are A and B independent?
- Yes
- - If independent
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P(A) = 0.3
P(B) = 0.5
Are A and B mutually exclusive?
- No
 - If mutually exclusive
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In a probability matrix, what does the bottom right corner contain?
1.00 meaning 100%
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- If mutually exclusive
