Suppose a hundred people (including yourself) have ordered sandwiches, and they are now rcady 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, instead of grabbing their sandwich, rudcly grabs one at random from the pile. As pcople 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 pcople ahcad 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 rudencss? 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.
Suppose a hundred people (including yourself) have ordered sandwiches, and they are now rcady 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, instead of grabbing their sandwich, rudcly grabs one at random from the pile. As pcople 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 pcople ahcad 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 rudencss? 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text:What is R(100)?
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