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Unformatted text preview: 1.2. DISCRETE PROBABILITY DISTRIBUTIONS 27 What is the probability of getting neither snakeeyes (double ones) nor boxcars (double sixes)? The event of getting either one of these two outcomes is the set E = { (1 , 1) , (6 , 6) } . Hence, the probability of obtaining neither is given by P ( ˜ E ) = 1 P ( E ) = 1 2 36 = 17 18 . In the above coin tossing and the dice rolling experiments, we have assigned an equal probability to each outcome. That is, in each example, we have chosen the uniform distribution function. These are the natural choices provided the coin is a fair one and the dice are not loaded. However, the decision as to which distribution function to select to describe an experiment is not a part of the basic mathemat ical theory of probability. The latter begins only when the sample space and the distribution function have already been defined. Determination of Probabilities It is important to consider ways in which probability distributions are determined in practice. One way is by symmetry. For the case of the toss of a coin, we do not see any physical difference between the two sides of a coin that should affect the chance of one side or the other turning up. Similarly, with an ordinary die therechance of one side or the other turning up....
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 Spring '09
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