Unformatted text preview: STAT 2023 - Holbrook From Randomness to Probability
Chapter 14 14 - 1 Trials & Outcomes
STAT 2023 - Holbrook 1. Trial Process of obtaining an outcome. 2. Outcome The individual possibility that occurs on
each 3. Event Specific collection of outcomes. 4. Sample Space (S) 14 - 2 Collection of all possible outcomes.
Collection all Outcome Examples
STAT 2023 - Holbrook Trial Sample Space Toss a Coin, Note Face
Toss 2 Coins, Note Faces
Select 1 Card, Note Kind
Select 1 Card, Note Color
Play a Football Game
Inspect a Part, Note Quality
Observe Gender Head, Tail
HH, HT, TH, TT
2♥, 2♦, ..., A♠ (52)
Win, Lose, Tie
Male, Female 14 - 3 Event Examples
STAT 2023 - Holbrook Trial: Toss 2 Coins. Note Faces.
1 Head & 1 Tail
Heads on 1st Coin
At Least 1 Head
Heads on Both
14 - 4 Outcomes in Event
HH, HT, TH, TT
HH, HT, TH
HH STAT 2023 - Holbrook Probabilities 14 - 5 What is Probability?
STAT 2023 - Holbrook 1. Numerical measure of
likelihood that an outcome
or event will occur.
or P(A) 2. Lies Between 0 & 1
2. Lies 1 Certain .5
.5 3. Sum of Probabilities is 1
14 - 6 Impossible STAT 2023 - Holbrook Assigning Event Probabilities 1. a priori Classical
2. Relative Frequency
Probability 14 - 7 What’s the
probability? a priori Classical Method
STAT 2023 - Holbrook 1. Prior Knowledge of the
2. Before Experiment 3. P(Event) = X / T
(Event) 14 - 8 X = No. of Event Outcomes
T = Total Outcomes in Sample Space
Each of T Outcomes Is Equally Likely P(Outcome) = 1/T © 1984-1994 T/Maker Co. STAT 2023 - Holbrook Relative Frequency Method 1. Actual Data Collected
2. Probability is determined
after the trial.
3. P(Event) = X / T
(Event) Repeat the trial
Event Observed X Times
Event 14 - 9 Of 100 Parts
Defects! Law of Large Numbers
STAT 2023 - Holbrook • • Long-run relative frequencies of
repeated independent trials get closer
and closer to the TRUE relative
frequency as the number of trials
Allows us to use the relative frequency
method with assurance.
method 14 - 10
10 STAT 2023 - Holbrook Personal Probability Method 1. Also called the Subjective Method.
2. Probabilities obtained by personal
assessment and experience.
3. Probabilities are NOT based on relative
frequencies or a priori probabilities.
priori 14 - 11
11 STAT 2023 - Holbrook Addition Rule for Disjoint Events 1. For Disjoint Events
• Events that do not occur simultaneously 2. P(A OR B) = P(A ∪ B) = P(A) + P(B)
P(A 14 - 12
12 STAT 2023 - Holbrook Multiplication Rule for Independent Events 1. For Independent Events
• Independence defined in Chapter 15. 2. P(A AND B) = P(A ∩ B) = P(A)*P(B)
AND 14 - 13
13 Statistical Independence
STAT 2023 - Holbrook 1.
Does Not Affect Probability
of Another Event
2. 14 - 14
14 Toss 1 Coin Twice
Finding a red light today
and finding a red light
tomorrow Causality Not Implied Complement Rule
STAT 2023 - Holbrook 1. Complement of Event For Event A, All Events Not In A: AC 2. Example: Let A be the event that you
pass this class and P(A)=0.80 What is
the the probability of NOT passing this
class; or what is P(AC)?
3. P(AC) = 1 – P(A) also, P(A) = 1 – P(AC)
14 - 15
15 End of Chapter
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