(a) Suppose you've hired 10 employees and each employee has a 0.3 probability of needing a new com- puter. Suppose this is independent for each employee. What is the probability that 4 employees will need new computers? Actually calculate the probability for this problem on a calculator; this is one of the rare times I'll ask you to do that. (b) Now, let's do the same problem, only you have 1,000 employees, and the probability of an employee has decreased to 0.003. (We still want to know the probability that exactly 4 employees need new computers.) Again, actually type it into a calculator. (c) Great, let's do the same thing now with 100,000 employees and 0.00003 probability of needing a computer. (d) Finally, consider a Poisson distribution with rate A = 3. What is the probability this Poisson random variable equals 4? (Again, please humor me and actually calculate the value.)
(a) Suppose you've hired 10 employees and each employee has a 0.3 probability of needing a new com- puter. Suppose this is independent for each employee. What is the probability that 4 employees will need new computers? Actually calculate the probability for this problem on a calculator; this is one of the rare times I'll ask you to do that. (b) Now, let's do the same problem, only you have 1,000 employees, and the probability of an employee has decreased to 0.003. (We still want to know the probability that exactly 4 employees need new computers.) Again, actually type it into a calculator. (c) Great, let's do the same thing now with 100,000 employees and 0.00003 probability of needing a computer. (d) Finally, consider a Poisson distribution with rate A = 3. What is the probability this Poisson random variable equals 4? (Again, please humor me and actually calculate the value.)
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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Transcribed Image Text:Problem 3.
(a) Suppose you've hired 10 employees and each employee has a 0.3 probability of needing a new com-
puter. Suppose this is independent for each employee. What is the probability that 4 employees will
need new computers? Actually calculate the probability for this problem on a calculator; this is one
of the rare times I'll ask you to do that.
(b) Now, let's do the same problem, only you have 1,000 employees, and the probability of an employee
has decreased to 0.003. (We still want to know the probability that exactly 4 employees need new
computers.) Again, actually type it into a calculator.
(c) Great, let's do the same thing now with 100,000 employees and 0.00003 probability of needing a
computer.
(d) Finally, consider a Poisson distribution with rate A = 3. What is the probability this Poisson random
variable equals 4? (Again, please humor me and actually calculate the value.)
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