Fundamental Concepts of Probability
Probability Concepts
1. Fundamental Concepts of Probability
2. Mutually Exclusive and Collectively
Exhaustive
3. Statistically Independent and Dependent
Events
4. Bayes’Theorem
Learning Objectives
• Understand the basic foundations of probability analysis • Learn the probability rules for conditional probability and joint probability
• Use Bayes’ theorem to establish posterior probabilities Reference: Text Chapter 2
Introduction
• Life is uncertain; we are note sure what the future will being
• Probability is a numerical statement about the likelihood that an event will occur
Fundamental Concepts
• The probability, P, of any event or state of nature occurring is greater than or equal to 0 and less than or equal to 1. That is:
0 ≤ P (event) ≤ 1
• The sum of the simple probabilities for all possible outcomes of an activity must equal 1
Example 1: Diversey Paint
• Demand for white latex paint at Diversey Paint and Supply has always been either 0, 1, 2, 3, or 4 gallons per day
• Over the past 200 days, the owner has observed the following frequencies of demand
QUANTITY
DEMANDED
NUMBER OF DAYS
PROBABILITY
0
40
0.20 (= 40/200)
1
80
0.40 (= 80/200)
The individual probabilities are all between 0 and 1
2
50
0.25 (= 50/200)
20
0.10 (= 20/200)
Determining objective probability:
• Relative frequency
– Typically based on historical data
P (event) =
0 ≤ P (event) ≤ 1
3
Types of Probability
4
10
Total
200
– Logically determine probabilities without trials
1
2
Number of ways of getting a head
Number of possible outcomes (head or tail)
The total of all event probabilities equals 1
∑ P (event) = 1.00
Types of Probability
Subjective probability is based on the experience and judgment of the person making the estimate
– Opinion polls
– Judgment of experts
Total number of trials or outcomes
• Classical or logical method
P (head) =
0.05 (=
1. Fundamental Concepts of Probability
2. Mutually Exclusive and Collectively
Exhaustive
3. Statistically Independent and Dependent
Events
4. Bayes’Theorem
Learning Objectives
• Understand the basic foundations of probability analysis • Learn the probability rules for conditional probability and joint probability
• Use Bayes’ theorem to establish posterior probabilities Reference: Text Chapter 2
Introduction
• Life is uncertain; we are note sure what the future will being
• Probability is a numerical statement about the likelihood that an event will occur
Fundamental Concepts
• The probability, P, of any event or state of nature occurring is greater than or equal to 0 and less than or equal to 1. That is:
0 ≤ P (event) ≤ 1
• The sum of the simple probabilities for all possible outcomes of an activity must equal 1
Example 1: Diversey Paint
• Demand for white latex paint at Diversey Paint and Supply has always been either 0, 1, 2, 3, or 4 gallons per day
• Over the past 200 days, the owner has observed the following frequencies of demand
QUANTITY
DEMANDED
NUMBER OF DAYS
PROBABILITY
0
40
0.20 (= 40/200)
1
80
0.40 (= 80/200)
The individual probabilities are all between 0 and 1
2
50
0.25 (= 50/200)
20
0.10 (= 20/200)
Determining objective probability:
• Relative frequency
– Typically based on historical data
P (event) =
0 ≤ P (event) ≤ 1
3
Types of Probability
4
10
Total
200
– Logically determine probabilities without trials
1
2
Number of ways of getting a head
Number of possible outcomes (head or tail)
The total of all event probabilities equals 1
∑ P (event) = 1.00
Types of Probability
Subjective probability is based on the experience and judgment of the person making the estimate
– Opinion polls
– Judgment of experts
Total number of trials or outcomes
• Classical or logical method
P (head) =
0.05 (=