LrTrChVIIISVConditionalProba - Math131(043)8.5:Conditional...

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Math131(043)8.5:Conditional Prob.Pg:1 8 . 5 : Conditional Probability Formula for Conditional Probability: If E and F are events associated with an equiprobable sample space and F , then P E | F # E F # F . It is shown that P E c | F 1 P E | F . Definition: The conditional probability of an event E , given that event F has occurred, is denoted P E | F and is defined by P E | F P E F P F if P F 0. Similarly, P F | E P E F P E if P E 0. General Multiplication Law: P E F P E P F | E P F P E | F . 1.437TAN15. A pair of fair dice is cast. What is the probability that the sum of the numbers falling uppermost is less than 9, 1
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Math131(043)8.5:Conditional Prob.Pg:2 if it is known that one of the number is 6? Solution. Sample space: 1,1 , 1,2 ,..., 1,6 , 2,1 ,..., 2,6 ,..., 6,1 , 6,2 ,..., 6,6 . Let A denote the event that the sum of the numbers is less than 9 and let B denote the event that one of the number is a 6. B  1,6 , 2,6 ,..., 6,6 , 6,1 , 6,2 ,..., 6 A B  1,6 , 6,1 , 2,6 , 6,2  Then, P A / B n A B n B 4/36 11/36 4 11 . 2.437TAN19. PRODUCT RELIABILITY . The probability that a battery will last 10 hr. or more is 0.80 , and the probability that it will last 15 hr. or more is 0.15. Given that a battery has lasted 10 hr. or more, find the probability that it will last 15 2
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Math131(043)8.5:Conditional Prob.Pg:3 hr. or more? Solution. Let A denote the event that the battery lasts 10 or more hours and let B denote the event that the battery lasts 15 or more hours. Then P A 0.8, P B 0.15 and P A B 0.15. Si nce B A Therefore, the probability that the battery will last 15 hours or more is P B / A P A B P A 0.15 0.8 3 16 0.1875. 3.437TAN21. Five black balls and four white balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a white ball if: a. The second ball is drawn without 3
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Math131(043)8.5:Conditional Prob.Pg:4 replacing the first? a. The probability that the second ball
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LrTrChVIIISVConditionalProba - Math131(043)8.5:Conditional...

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