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Unformatted text preview: 4.1 (cont.) Probability Models The Equally Likely Approach (also called the Classical Approach) Assigning Probabilities If an experiment has N outcomes, then each outcome has probability 1/N of occurring If an event A 1 has n 1 outcomes, then P(A 1 ) = n 1 /N Dice You toss two dice. What is the probability of the outcomes summing to 5? There are 36 possible outcomes in S , all equally likely (given fair dice). Thus, the probability of any one of them is 1/36. P (the roll of two dice sums to 5) = P (1,4) + P (2,3) + P (3,2) + P (4,1) = 4 / 36 = 0.111 This is S : {(1,1), (1,2), (1,3), etc.} We Need Efficient Methods for Counting Outcomes Product Rule for Ordered Pairs A student wishes to commute to a junior college for 2 years and then commute to a state college for 2 years. Within commuting distance there are 4 junior colleges and 3 state colleges. How many junior collegestate college pairs are available to her? Product Rule for Ordered Pairs junior colleges: 1, 2, 3, 4 state colleges a, b, c possible pairs: (1, a) (1, b) (1, c) (2, a) (2, b) (2, c) (3, a) (3, b) (3, c) (4, a) (4, b) (4, c) Product Rule for Ordered Pairs junior colleges: 1, 2, 3, 4 state colleges a, b, c possible pairs: (1, a) (1, b) (1, c) (2, a) (2, b) (2, c) (3, a) (3, b) (3, c) (4, a) (4, b) (4, c) 4 junior colleges 3 state colleges total number of possible pairs = 4 x 3 = 12 Product Rule for Ordered Pairs junior colleges: 1, 2, 3, 4 state colleges a, b, c possible pairs: (1, a) (1, b) (1, c)...
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 Spring '08
 reiland

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