D2 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 intabular 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 diabeticpatients receiving insulin develops antibodies against the hormone, thus, requiring amore costly form of medication.a. Find the probability that in the next five patients the researcher treats, none willdevelop 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. Ifthe number of available beds today is 4 beds for new patients, what is the probabilitythat 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 Poissondistribution with a mean value of 1.5.A. Calculate the probability that exactly three escapes will be attempted during thenext month.B. Calculate the probability that exactly one escape will be attempted during the nextmonth.E. Exercises ( Geometric Probability Distribution)1. An oil company has determined that the probability of finding oil at a particulardrilling operation is 0.20. What is the probability that it would drill four dry wells beforefinding oil at the fifth one?

Answered: Image /qna-images/answer/318effcf-317a-4e11-a3de-acd0b3b4a982.jpg

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

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

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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