MATH
SC8SN

# 2 for each trial there are two mutually exclusive

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Each repetition is called a trial. 2. For each trial there are two mutually exclusive (disjoint) outcomes: success or failure 3. The trials are independent 4. The probability of success is the same for each trial of the experiment 5. We repeat the trials until we get a success Geometric PDF The geometric distribution addresses the number of trials necessary before the first success . If the trials are repeated k times until the first success, we will have had k – 1 failures. If p is the probability for a success and q = (1 – p) the probability for a failure, the probability for the first success to occur at the kth trial will be (where x = k ) P(x) = p(1 – p) x-1 , x = 1, 2, 3, … even though the geometric distribution is considered discrete, the x values can theoretically go to infinity Mean and Standard Deviation: TI-83 Support: For P(X = k) using the calculator: 2 nd VARS geometpdf(p,k) For P(k ≤ X) using the calculator: 2 nd VARS geometcdf(p,k) For P(X > k) use 1 – P(k ≤ X) or (1- p) k Examples of Geometric Probability Distribution: First car arriving at a service station that needs brake work Flipping a coin until the first tail is observed First plane arriving at an airport that needs repair Number of house showings before a sale is concluded Length of time(in days) between sales of a large computer system

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Chapter 8: The Binomial and Geometric Distributions Example 1: The probability for finding an error by an auditor in a production line is 0.01. What is the probability that the first error is found at the 70 th part audited? Example 2: What is the probability that more than 50 parts need to be audited before the first error is found? Homework: Day 1: pg 543 – 44, 8.41, 8.42
Chapter 8: The Binomial and Geometric Distributions Example 3: The drilling records for an oil company suggest that the probability the company will hit oil in productive quantities at a certain offshore location is 0.2. Suppose the company plans to drill a series of wells. a) What is the probability that the 4th well drilled will be productive (or the first success by the 4th)? b) What is the probability that the 7th well drilled is productive (or the first success by the 7th)? c) Is it likely that x could be as large as 15(or the first success by the 15th)? d) Find the mean and standard deviation of the number of wells that must be drilled before the company hits its first productive well. Example 4: An insurance company expects its salespersons to achieve minimum monthly sales of \$50,000. Suppose that the probability that a particular salesperson sells \$50,000 of insurance in any given month is .84. If the sales in any one- month period are independent of the sales in any other, what is the probability that exactly three months will elapse before the salesperson reaches the acceptable minimum monthly goal?

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