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M ARIO F . T RIOLA

S TATISTICS. E LEMENTARY. Section 3-4 Multiplication Rule: Basics. M ARIO F . T RIOLA. E IGHTH. E DITION. Finding the Probability of Two or More Selections. Multiple selections Multiplication Rule. Notation. P(A and B) = P(event A occurs in a first trial and

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M ARIO F . T RIOLA

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  1. STATISTICS ELEMENTARY Section 3-4 Multiplication Rule: Basics MARIO F. TRIOLA EIGHTH EDITION

  2. Finding the Probability of Two or More Selections • Multiple selections • Multiplication Rule

  3. Notation P(A and B) = P(event A occurs in a first trial and event B occurs in a second trial)

  4. FIGURE 3-9 Tree Diagram of Test Answers Ta Tb Tc Td Te Fa Fb Fc Fd Fe a b c d e a b c d e T F

  5. FIGURE 3-9 Tree Diagram of Test Answers Ta Tb Tc Td Te Fa Fb Fc Fd Fe a b c d e a b c d e T F

  6. 1 2 FIGURE 3-9 Tree Diagram of Test Answers Ta Tb Tc Td Te Fa Fb Fc Fd Fe a b c d e a b c d e T F P(T) =

  7. 1 1 5 2 FIGURE 3-9 Tree Diagram of Test Answers Ta Tb Tc Td Te Fa Fb Fc Fd Fe a b c d e a b c d e T F P(T) = P(c) =

  8. 1 1 1 5 2 10 FIGURE 3-9 Tree Diagram of Test Answers Ta Tb Tc Td Te Fa Fb Fc Fd Fe a b c d e a b c d e T F P(T) = P(c) = P(T and c) =

  9. P (both correct)

  10. P (both correct) = P (T and c)

  11. 1 10 P (both correct) = P (T and c) 1 1 2 5

  12. 1 10 P (both correct) = P (T and c) 1 1 = • 2 5 Multiplication Rule

  13. 1 10 P (both correct) = P (T and c) 1 1 = • 2 5 Multiplication Rule INDEPENDENT EVENTS

  14. Notation for Conditional Probability P(B A) represents the probability of event B occurring after it is assumed that event A has already occurred (read B A as “B given A”).

  15. Definitions • Independent Events Two events A and B are independent if the occurrence of one does not affect the probability of the occurrence of the other. • Dependent Events If A and B are not independent, they are said to be dependent.

  16. Formal Multiplication Rule • P(A and B) = P(A) • P(B A) • If A and B are independent events, P(B A) is really the same as P(B)

  17. Figure 3-10 Applying the Multiplication Rule P(A or B) Multiplication Rule Are A and B independent ? Yes P(A and B) = P(A) • P(B) No P(A and B) = P(A) • P(B A)

  18. Intuitive Multiplication When finding the probability that event A occurs in one trial and B occurs in the next trial, multiply the probability of event A by the probability of event B, but be sure that the probability of event B takes into account the previous occurrence of event A.

  19. Small Samples from Large Populations If a sample size is no more than 5% of the size of the population, treat the selections as being independent (even if the selections are made without replacement, so they are technically dependent).

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