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What is R(1000)?

What is R(1000)?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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What is R(1000)?

Suppose a hundred people (including yoursclf) have ordered sandwiches, and they are now ready to be picked up. Everyone has ordered a distinct sandwich, and they are all clearly labeled. People file in one at a time to pick up their sandwich. You are last in line, unfortunately, because you were busy doing probability homework late last night and didn't get to the sandwich shop until late. However, the first person in line is having a worse day than you, and in a rush and huff, instcad of grabbing their sandwich, rudely grabs one at random from the pile. As people file in, if their sandwich is there they take it, but if it is not, then they (frustrated) simply grab one at random from the pile. You've got 99 people ahead of you, and plenty of time to obscrve this in action. Given your affection for probability, you immediately start to wonder: what is the probability that you are going to be able to get your own sandwich, free from the corrupting influence of the first customer's rudeness? Consider generalizing in the following way: N customers line up for their sandwiches, and you are the last customer in line; the first customer grabs a sandwich at random, and every customer afterwards attempts to take their own sandwich, or will grab one at random. Define R(N) to be the probability that you get your own sandwich in this situation.
Transcribed Image Text:Suppose a hundred people (including yoursclf) have ordered sandwiches, and they are now ready to be picked up. Everyone has ordered a distinct sandwich, and they are all clearly labeled. People file in one at a time to pick up their sandwich. You are last in line, unfortunately, because you were busy doing probability homework late last night and didn't get to the sandwich shop until late. However, the first person in line is having a worse day than you, and in a rush and huff, instcad of grabbing their sandwich, rudely grabs one at random from the pile. As people file in, if their sandwich is there they take it, but if it is not, then they (frustrated) simply grab one at random from the pile. You've got 99 people ahead of you, and plenty of time to obscrve this in action. Given your affection for probability, you immediately start to wonder: what is the probability that you are going to be able to get your own sandwich, free from the corrupting influence of the first customer's rudeness? Consider generalizing in the following way: N customers line up for their sandwiches, and you are the last customer in line; the first customer grabs a sandwich at random, and every customer afterwards attempts to take their own sandwich, or will grab one at random. Define R(N) to be the probability that you get your own sandwich in this situation.
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