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E. Exercises ( Geometric Probability Distribution) 1. An oil company has determined that the probability of finding oil at a particular drilling operation is 0.20. What is the probability that it would drill four dry wells before finding oil at the fifth one?

E. Exercises ( Geometric Probability Distribution) 1. An oil company has determined that the probability of finding oil at a particular drilling operation is 0.20. What is the probability that it would drill four dry wells before finding oil at the fifth one?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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C. Exercises (Binomial Probability Distribution) 1. Suppose X is a binomial random variable with n= 4 and p = 0.2. Calculate P(x) for each of the following values of x = 0, 1, 2, 4. Give the probability distribution in tabular form. 2. Suppose X is a binomial random variable with n = 5 and p = 0.5. a. DisplayP(x) in tabular form. b. Compute the mean and the variance of x. 3. Over the years, a medical researcher has found that one out of every ten diabetic patients receiving insulin develops antibodies against the hormone, thus, requiring a more costly form of medication. a. Find the probability that in the next five patients the researcher treats, none will develop antibodies against insulin. b. Find the probability that at least one will develop antibodies. D. Exercises (Poisson Probability Distribution) 1. The mean number of patients entering an emergency room at a hospital is 2.5. If the number of available beds today is 4 beds for new patients, what is the probability that the hospital will not have enough beds to accommodate its new patients? 2. A prison reports that the number of escape attempts per month has a Poisson distribution with a mean value of 1.5. A. Calculate the probability that exactly three escapes will be attempted during the next month. B. Calculate the probability that exactly one escape will be attempted during the next month. E. Exercises ( Geometric Probability Distribution) 1. An oil company has determined that the probability of finding oil at a particular drilling operation is 0.20. What is the probability that it would drill four dry wells before finding oil at the fifth one?
Transcribed Image Text:C. Exercises (Binomial Probability Distribution) 1. Suppose X is a binomial random variable with n= 4 and p = 0.2. Calculate P(x) for each of the following values of x = 0, 1, 2, 4. Give the probability distribution in tabular form. 2. Suppose X is a binomial random variable with n = 5 and p = 0.5. a. DisplayP(x) in tabular form. b. Compute the mean and the variance of x. 3. Over the years, a medical researcher has found that one out of every ten diabetic patients receiving insulin develops antibodies against the hormone, thus, requiring a more costly form of medication. a. Find the probability that in the next five patients the researcher treats, none will develop antibodies against insulin. b. Find the probability that at least one will develop antibodies. D. Exercises (Poisson Probability Distribution) 1. The mean number of patients entering an emergency room at a hospital is 2.5. If the number of available beds today is 4 beds for new patients, what is the probability that the hospital will not have enough beds to accommodate its new patients? 2. A prison reports that the number of escape attempts per month has a Poisson distribution with a mean value of 1.5. A. Calculate the probability that exactly three escapes will be attempted during the next month. B. Calculate the probability that exactly one escape will be attempted during the next month. E. Exercises ( Geometric Probability Distribution) 1. An oil company has determined that the probability of finding oil at a particular drilling operation is 0.20. What is the probability that it would drill four dry wells before finding oil at the fifth one?
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