AF Chaper 5 handouts

AF Chaper 5 handouts - 9/18/2008 STAT 2000 Terminology and...

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9/18/2008 1 STAT 2000 Chapter 5 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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9/18/2008 2 You try: Toss two balanced coins. What is the sample space? What is the probability of getting two heads? What is the probability of getting exactly one head? What is the probability of getting two of a kind? Properties of Probabilities The probability of any outcome in the sample space is between 0 and 1.
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AF Chaper 5 handouts - 9/18/2008 STAT 2000 Terminology and...

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