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# lect2 - EXAMPLE DICE SAMPLE SPACE AND EVENTS PROBABILITY...

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EXAMPLE: DICE SAMPLE SPACE AND EVENTS PROBABILITY AND ITS FREQUENCY INTERPRETATION Outline EXAMPLE: DICE SAMPLE SPACE AND EVENTS PROBABILITY AND ITS FREQUENCY INTERPRETATION MARK SIX PROBABILITY MODELS 1 / 14 Xinghua Zheng Lect 2: Axioms of Probability

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EXAMPLE: DICE SAMPLE SPACE AND EVENTS PROBABILITY AND ITS FREQUENCY INTERPRETATION EXAMPLE: DICE Two dice, one white and the other black, are to be rolled. The possible ways for the 2 dice to fall are: There are ways in all. Assuming that the dice are fair, the chance to roll a total of 5 is . 2 / 14 Xinghua Zheng Lect 2: Axioms of Probability
EXAMPLE: DICE SAMPLE SPACE AND EVENTS PROBABILITY AND ITS FREQUENCY INTERPRETATION EXAMPLE: DICE ( ctd) The chance that the black die is an ace ( ) equals . The chance that both dice are aces equals . The chance that at least one die is an ace equals . The chance that neither die is an ace equals . The chance both dice show the same number equals . The chance the number on the white die is strictly greater than the number on the black die equals . 3 / 14 Xinghua Zheng Lect 2: Axioms of Probability

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EXAMPLE: DICE SAMPLE SPACE AND EVENTS PROBABILITY AND ITS FREQUENCY INTERPRETATION TERMINOLOGY The collection of all possible outcomes of some chance process is called the sample space , denoted by S or Ω . A subset E of the sample space is called an event . If the outcome of the chance process is in E, one says that E occurs . If E doesn’t occur, then the complementary event E c does. 4 / 14 Xinghua Zheng Lect 2: Axioms of Probability
EXAMPLE: DICE SAMPLE SPACE AND EVENTS PROBABILITY AND ITS FREQUENCY INTERPRETATION THE LANGUAGE OF EVENTS .

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