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Finite Chapter 7.2 - Math 120 SP08 SBrodnick 7.2 Estimated...

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Math 120 SP08 SBrodnick 1 1 7.2 : Estimated & Theoretical Probability 2 7.2: Estimated & Theoretical Probability * Estimated Probability is based on actual data * Theoretical Probability is based on intuition *Est. Prob. of event E: P(E) = *Theoretical Prob. of event E: P(E) = frq(E) N # of times event E occurs (frequency of E) # of times experiment is performed (# of trials / sample size) # of favorable outcomes total # of possible outcomes = n(E) n(S) 3 * Collection of all of the outcomes and their probabilities: * Properties : 1. Prob. of each outcome is a number between 0 and 1 (including 0 & 1) 2. Prob.’s of all events add up to 1 3. Prob. of an event E is the sum of the prob.’s of individual outcomes in E 7.2: Estimated & Theoretical Probability Probability Distribution 4 Examples : 1. Toss a coin 100 times Event E: Heads You toss heads 43 times P ( E ) = ? 2.A die is rolled 50 times. The frequency of each roll is listed below. Find the est. prob. distribution . Roll: 1 2 3 4 5 6 Freq: 9 11 6 10 6 8 7.2: Estimated & Theoretical Probability 5 3.
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