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A probability model for a particular experiment is a probability distribution that predicts the relative frequency of each outcome if the experiment is performed a large number of times Just as we occasionally refer to relative frequency as estimated probability we occasionally refer to modeled probability as theoretical probability Examples 1 Fair Coin Model See Example 2 above Flip a fair coin and observe the side that faces up Because we expect that heads is as likely to come up as tails we model this experiment with the probability distribution specified by SS H T P H 5 P T 5 2 Unfair Coin Model See Example 3 above Take SS H T P H 2 P T 8 We can think of this distribution as a model for the experiment of flipping an unfair coin that is four times as likely to land with tails uppermost than heads 3 Fair Die Model Roll a fair die and observe the uppermost number Because we expect to roll each specific number one sixth of the time we model the experiment with the probability distribution specified by S 1 2 3 4 5 6 P 1 1 6 P 2 1 6 P 6 1 6 4 Two Dice Model Roll a pair of fair dice recall that there are a total of 36 outcomes if the dice are distinguishable Then an appropriate model of the experiment has S 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 with each outcome being assigned a probability of 1 36 5 Look at the preceding example and take E to be the event that the sum of the numbers that face up is 3 so E 1 2 2 1 QBy the properties of probability distributions P E Check Hint Clear

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