Review Ch - Professors name is Lisa Mackay PDF

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Professors name is Lisa Mackay
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Ch.5 Experiment: is a process that produces outcomes Sample Space: Possible outcome from an experiment Event: an event is an individual outcome of a sample space Simple Event: Single outcome that cannot be broken down Range of possible probabilities: 0≥P(E)≤1 Sum of probabilities of all outcomes: ∑P(X)=1 There are three methods of assigning probabilities 1. The classical method 2. The relative frequency method 3. Subjective Probability Classical Method: The probability of various events can be determined before the fact. This approach requires equally likely outcomes. (We know the outcomes are = Likely) P(E) =

ne N

ne : number of outcomes for your event N: your total possible outcome for your experiment Example 1: In a deck of cards, what is the probability of drawing a spade? Solution: P(Spade) =

ne N

=

13 52

= 0.25 (there are 13 spades in a deck of cards)

Relative Frequency Method: Probability is based on accumulated historical data. P(E)=

Total Number of opportunites for the Event Number of ׿ Event Occured Occur ¿ ¿

Example 2: Ten of the 500 randomly selected cars manufactured at a factory are found to have electrical problems. Assuming the electrical problems occur randomly, what is the probability that the next car manufactured at this factory will have electrical problems? Soultion: P(electrical)=

ne N

=

10 500

= 0.02

15000 x 0.02 = 300

Subjective Probability: The available options and information are evaluated, and the probability is eliminated.

Probability Matrix: It’s a chart or table that contains all available joint and marginal probabilities for a question

A

B Where they cross

Joint Probability: This is the probability of intersection

P(AnB) Joint (and)

Marginal Probability: This is the probability of an event with no extra overlaps or exclusions

P(A)

Example: Probability someone wears glasses in BSTAT count total people, what is the probability someone wearing glasses and hats.

Conditional Probability: Is one that comes with conditional brief

P( AnB ) P( B) P(A/B) =

P(A B) =

– Probability of a “given” that B has already happened “If”, “Or”

P( AnB ) P( B)

OR

P(B/A)=

If Among

P( BnA ) P( A)

Union Probability: P(AuB) The union of A, B is formed by combining elements from both sets: AuB read “A or B” Multiplication Rule: Is just the conditional probability formula rearranged P(AnB) = P(A) · P(B/A) Or equivalently P(BnA) = P(B)· P(A/B)

*The multiplication rule formula is just the conditional probability formula rearranged

*If A and B are independent the formula simplifies to: P(AnB) =P(A)·P(B) Additional Rule: Union Probability for addition rule keyword: “OR” P(AuB) =P(A) +P(B) -P(AnB) = ”or” Mutually exclusive events are events with no common outcomes: P(AnB)=0 *If A and B are mutually exclusive (have no overlap) the formula simplifies to: P(AuB) =P(A)+ P(B) Probability Trees:

*We will focus less on probability trees than probability matrices but will look at both....