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Chapter 5 (Sp12) - Section 5.1 Probability Rules...

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Section 5.1 –Probability Rules Probability – a measure of the likelihood of a random phenomenon or chance behavior. Probability deals with experiments that yield short-term results (outcomes) and reveal long-term predictability. The long-term proportion with which a certain outcome is observed is the probability of that outcome. Law of Large Numbers As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome. Sample Space – The collection of all possible outcomes. Denoted S. Event – A collection of outcomes from a probability experiment. (may consist of one or more outcomes) Events are usually denoted with capital letters. P(E) means the “probability that event E occurs” Probability Rules : 1. For any event E, ____ ≤ P(E) ≤ ____ . 2. An impossible event has probability ________. 3. An event certain to occur has probability ________. 4. The sum of the probabilities of all outcomes must equal _____. 5. An event with a probability less than 0.05 (5%) is considered _________________ . Different Ways to Compute Probability : 1. Approximating Probabilities using the Empirical Approach : Perform a procedure a large number of times and record how many times event A occurs. P(E) = eriment the in trials of number occurs E times of number exp Example : During his career, Reggie Miller made 5915 of 6679 free throw attempts after being fouled. Find the probability that Reggie Miller will make a free throw after being fouled. Example : In a movie theater, 50 people have popcorn and 35 people do not. What is the probability that a randomly selected person has popcorn? 1
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A probability model lists all possible outcomes of a probability experiment along with each outcome’s probability. Example : Build a probability model for cola preference in your class. Would it be unusual to randomly select an individual who likes Pepsi? 2. Computing Probabilities Using the Classical Method : Each simple event must have an equal chance of occurring (ie, outcomes must be equally likely ) P(E) = outcomes possible of number occur can E ways of number Example : A multiple choice test has 5 choices for each problem. What is the probability that if you guess, you will guess incorrectly? Example : Roll 2 dice. What is the probability of getting a sum of 9? What is the probability of getting a sum of 7? Favorite Cola Frequency Probability Coke Pepsi Dr. Pepper 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 2
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Example : If a person is randomly selected, find the probability that his or her birthday is September 26 th . Find the probability that his or her birthday is in December. Example : A roulette wheel has 38 slots (0, 00, 1–36). You bet on an odd number. a) P(win) = b) P(lose) = Many times it is helpful if you create a tree diagram to create the sample space.
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