ch12MGF1106 - Slide 12 - 1 Chapter 12 Probability Slide 12...

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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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This note was uploaded on 12/12/2011 for the course MGF 1106 taught by Professor Holbrook during the Spring '10 term at Santa Fe College.

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ch12MGF1106 - Slide 12 - 1 Chapter 12 Probability Slide 12...

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