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 uptheir sandwich. You are last in line, unfortunately, because you were busy doing probability homework late last nightand 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 theirsandwich, rudely grabs one at random from the pile. As people file in, if their sandwich is there they take it, but ifit is not, then they (frustrated) simply grab one at random from the pile. You've got 99 people ahead of you, andplenty 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 tobe 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 customerin line; the first customer grabs a sandwich at random, and every customer afterwards attempts to take their ownsandwich, or will grab one at random. Define R(N) to be the probability that you get your own sandwich in thissituation.

In this problem, we are analyzing a scenario where a hundred people, including the observer, have…

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What is R(1000)?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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Question

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.

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