CJUS-K300 1nd Edition Lecture 7 Outline of Last Lecture I. ProbabilityOutline of Current Lecture II. Multiplication RuleIII. Conditional ProbabilitiesIV. Independent eventsCurrent LectureThird rule of probability: Multiplication Rule (general form) - P(A and B) = P(A) x P(B|A) Conditional Probabilities - P(A|B): the probability that A will happen given that B has already happened- P(B|A): the probability that B will happen given that A has already happened. P(A and B) = P (A) x P(B|A)Example: State # of HomicidesIllinois 12 - Central City 9 - Suburban 2- Rural 1Michigan 9 - Central City 5These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Suburban 1- Rural 3Texas 16- Central City 11 - Suburban 3- Rural 2Total 37What is the probability of P(Michigan and Rural)P(MI) x P(Rural|Michigan) = 9/37 x 3/9 = .24 X 33 = .08P (IL and Suburban) = P(IL) x P(IL|Suburban) = 12/37 x 2/12 = .32 x .17 = .05- The nominator in the first term is always the denominator in the second term, cancellingeach other out. Independent Events- When two events are statistically independent, knowing that event A has already occurred does not help you at all in predicted the probability of event B occurring. A good example of this is in the deck of cards. Knowing the probability of drawing an Ace P(Ace) does not help you figure out the probability of the suit of the Ace P(Heart). For statistically independent event P(A|B) = P(A) and P(B|A) = P(B)The short form of the Multiplication Rule, which can ONLY be used for Independent events - P(A and B) = P(A) x P(B) How do we know which events are statistically independent?If P(A|B) = P(A) then the events must be independent- Does P(Ace|Heart) = P(Ace)?o P(Ace|Heart) = 1/13 or .08o P(Ace) = 4/52 or.08o They are independent!- Which means that P(Ace and Heart) = P(Ace) X P(Heart)o 4/52 x 13/52 = .08 x .25 =
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