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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