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Understanding Probability Fundamentals: Rules, Notations, and Examples

Learn the basics of probability including the Addition Rule, Multiplication Rule, and simulating probabilities through examples. Understand the concepts of simple and compound events, sample space, and determining probabilities using relative frequency or classical approach.

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Understanding Probability Fundamentals: Rules, Notations, and Examples

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  1. Statistics 300:Introduction to Probability and Statistics Section 4-2

  2. Probability • Chapter 4 • Section 2: Fundamentals • Section 3: Addition Rule • Section 4: Multiplication Rule #1 • Section 5: Multiplication Rule #2 • Section 6: Simulating Probabilities • Section 7: Counting

  3. Fundamentals • Vocabulary (Terms) • Event • Simple Event • Sample Space

  4. Example Procedures • Roll a die; record value • Roll 2 dice; record sum • Survey 50 people; count “no’s” • Select 200 people at random; take heights; record average

  5. Event • The result of a procedure • Examples: • Value of die is 4 • Sum of 2 dice is 10 • The average height of 200 people is 64.83 inches

  6. Events: Simple or Compound • Simple • Can only occur in one way • Compound • Can occur in multiple ways

  7. Events: Simple or Compound • Examples: • Value of die is 4 : simple • Sum of 2 dice is 10 : compound • The avg. height of 200 people is 64.83 inches : compound

  8. Sample Space • The collection of all possible simple events • See EXCEL example for rolling two dice

  9. Notation for Probabilities • “P” denotes “the probability of” • A, B, C, etc. denote specific events • So we read “P(A)” as “the probability of A”

  10. Probability Notation(try some on overhead)

  11. What is a Probability? • No definition is universally accepted • Mine: A relative frequency that has not happened yet • Sophisticated math definitions • Degree of belief

  12. Determining Probabilities • Experience • Rule 1: Observe the relative frequency over many trials • Logic • Rule 2: Deduce the relative frequency based on principles

  13. Experience: Rule 1 • Relative Frequency Approximation of Probability • Conduct a procedure many times; observe the relative frequency • P(A) = (count A / total count)

  14. Try this:If I drop my right shoe from shoulder height, what is the probability that it will land upright?

  15. Logic: Rule 2 • Classical Approach to Probability • Determine the number of ways that event “A” can occur • Determine the number of all possible outcomes • P(A) = (ways for A)/(all ways)

  16. Try this:What is the probability that I will get a 6 when I roll a die?

  17. Complementary Events • The complement of event “A” consists of all possible outcomes for which “A” does not occur • Denoted “A” with a line over the top • P(A) is “Probability of not A” • A = a woman is selected, then • A = a woman is not selected

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