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Unformatted text preview: Slide 12  1 Chapter 12 Probability Slide 12  2 12.1 The Nature of Probability Slide 12  3 Definitions An experiment or trial is a controlled operation that yields a set of results. The possible results of an experiment are called its outcomes . An event is a subcollection of the outcomes of an experiment. Slide 12  4 Definitions continued Empirical probability is the relative frequency of occurrence of an event and is determined by actual observations of an experiment. Theoretical probability is determined through a study of the possible outcomes that can occur for the given experiment. Slide 12  5 Empirical Probability Example: In 100 tosses of a fair die, 19 landed showing a 3. Find the empirical probability of the die landing showing a 3. Let E be the event of the die landing showing a 3. P ( E ) = number of times event E has occurred total number of times the experiment has been performed P ( E ) = 19 100 = 0.19 Slide 12  6 Example 1 In a coin toss contest, Paul discovered that the coin landed heads up 44 times out of 100. What is the empirical probability of getting: i. Head ii. Tail Let H be the event the coin lands heads up and T the event the coin lands tails up. P(H) = P(T) = 4 4 1 1 1 0 0 2 5 = 1 1 1 4 1 ( ) 1 2 5 2 5 P H =  = Slide 12  7 Example 2 In a given week, a veterinarian treated the following animals, What is the empirical probability that the next animal she treats is a a. a dog b. a cat c. an iguana ANIMAL NUMBER TREATED Dog 40 Cat 35 Bird 15 Iguana 5 Slide 12  8 Example 2 a. The empirical probability that the next animal she treats is a dog is: b. The empirical probability that the next animal she treats is a cat is: ANIMAL NUMBER TREATED Dog 40 Cat 35 Bird 15 Iguana 5 TOTAL 95 40 8 95 19 = 35 7 95 19 = 5 1 95 19 = c. The empirical probability that the next animal she treats is an iguana is: Slide 12  9 The Law of Large Numbers The law of large numbers states that probability statements apply in practice to a large number of trials, not to a single trial. It is the relative frequency over the long run that is accurately predictable, not individual events or precise totals. Slide 12  10 12.2 Theoretical Probability Slide 12  11 Equally likely outcomes If each outcome of an experiment has the same chance of occurring as any other outcome, they are said to be equally likely outcomes . For equally likely outcomes, the probability of Event E may be calculated with the following formula. P ( E ) = number of outcomes favorable to E total number of possible outcomes Slide 12  12 Important Facts The probability of an event that cannot occur is 0. The probability of an event that must occur is 1....
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 Spring '10
 HOLBROOK
 Probability, Probability theory, Playing card, Tree Diagram

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