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AF Chaper 5 handouts

AF Chaper 5 handouts - STAT 2000 Terminology and...

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9/18/2008 1 STAT 2000 Chapter 5 P b bilit Probability Agresti-Franklin Terminology and Definitions : Tossing a coin would be considered a random phenomenon because the outcome is uncertain. It could be heads or it could be tails. Probability is a way of measuring this uncertainty is a way of measuring this uncertainty. If we toss a balanced coin 4 times, we are not assured of getting exactly two heads and two tails. But if we toss a balanced coin a large number of times … According to the Law of Large Numbers , if we repeatedly toss a balanced coin, the proportion of times a head will occur will get closer and closer to 0.5. We call this number the probability of getting a head head. In repeated trials of a random phenomenon, the proportion of times a certain outcome is observed will approach a number that we call the probability of that particular outcome. It is not always possible to repeat a random phenomenon a large number of times to determine objective information. Sometimes we have to rely on subjective probability. For example: If I drive to class today, what is the probability that I will find a parking place quickly? We also rely on probability properties and rules. Terminology and Examples A sample space is the set of all possible outcomes of a random phenomenon. (It is denoted S.) Ex: Toss a coin. Sample Space is {H, T} Ex: Toss a die. Sample Space is {1, 2, 3, 4, 5, 6} An event is a subset of the sample space. Ex: Toss a die. Let E be the event an even number is observed. E = {2, 4, 6} For the event E, getting an even number of dots on a die toss, P(E) = P(2) + P(4) + P(6) = 1/6 + 1/6 + 1/6 = 3/6 The probability of an event A is denoted P(A), and is determined by adding the probabilities of the individual outcomes in the event. E = {2,4,6} IF the individual outcomes are equally likely, P(A) = # of outcomes in the event A # of outcomes in the sample space = # of outcomes favorable to A total # of outcomes
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