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Section 4-2

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

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Section 4-2

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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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