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Unformatted text preview: Elementary Probability Theory MM207: Statistics Unit 4 Seminar LEARNING OUTCOMES Define probability and know how it relates to the outcomes of random events Understand how the probabilities of multiple events are related Use a tree diagram to display the outcomes of experiments consisting of multiple events Use counting techniques to determine the number of possible outcomes Statistics & Probability Statistics (p. 5): The study of how to collect, organize, analyze, and interpret numerical information Probability (p. 160): A numerical measure between 0 and 1 that describes the likelihood that an event will occur Probability & Its Complement Probability of an event # of favorable outcomes Total # of outcomes Given 2 red balls & 3 green balls Complement of a probability: the probability that it does not occur 2 P( red ball ) = 5 3 P (not red ball ) = 5 Probability of AND MULTIPLY Independent: P(A & B) = P(A)*P(B) P( red ball & green ball) if ball is replaced before the second one is chosen Dependent: P(A & B) = P(A)*P(B|A) P( red ball & green ball) if ball is not replaced before the second one is chosen Probability of OR ADD Mutually Exclusive P(A or B) = P(A) + P(B) NOT Mutually Exclusive P(A or B) = P(A) + P(B) P(A & B) See example on p. 178 Also, see p. 181 for general rules Tree Diagram
Toss a Coin 3 Times Permutation & Combination Permutation (ORDER matters) 7 people running in a race, how many different ways can someone finish first, second, third? P 7, 3 Combination (order does not matter) 7 people running in a race, how many different ways they finish the race? C 7, 3 ...
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- Spring '08