Suppose that an Enigma machine operator makes a mistake on one of every 80 letters transmitted on average independently of their mistakes on other letters. Today they have sent a 135-letter message. (a) Calculate the precise probability that the operator made a mistake on either 1 or 2 of the letters in this message. (b) Approximate the probability in (a) using the Poisson distribution. Do you think this approximation is a good one? Why?
Suppose that an Enigma machine operator makes a mistake on one of every 80 letters transmitted on average independently of their mistakes on other letters. Today they have sent a 135-letter message. (a) Calculate the precise probability that the operator made a mistake on either 1 or 2 of the letters in this message. (b) Approximate the probability in (a) using the Poisson distribution. Do you think this approximation is a good one? Why?
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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Question
Suppose that an Enigma machine operator makes a mistake on one of every 80 letters transmitted on average independently of their mistakes on other letters. Today they have sent a 135-letter message.
(a) Calculate the precise
(b) Approximate the probability in (a) using the Poisson distribution. Do you think this approximation is a good one? Why?
Expert Solution
Step 1
Suppose that an Enigma machine operator makes a mistake on one of every 80 letters transmitted
Let p = probability of making mistake =
q = probability of not making mistake = 1 - p =
Step by step
Solved in 3 steps
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