CJUS K300 1nd Edition Lecture 7 Outline of Last Lecture I Probability Outline of Current Lecture II Multiplication Rule III Conditional Probabilities IV Independent events Current Lecture Third 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 Homicides Illinois 12 Central City 9 Suburban 2 Rural 1 Michigan 9 Central City 5 These 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 3 Texas 16 Central City 11 Suburban 3 Rural 2 Total 37 What is the probability of P Michigan and Rural P MI x P Rural Michigan 9 37 x 3 9 24 X 33 08 P 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 cancelling each 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 08 o P Ace 4 52 or 08 o They are independent Which means that P Ace and Heart P Ace X P Heart o 4 52 x 13 52 08 x 25 02
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