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3. Show that for N > 2, R(N) satisfies the following: N-1 1 R(N) :> R(i) N . i=1 Hint: R(N) is the probability of the event. How can you break it down into smaller, more tractable probabilities?

3. Show that for N > 2, R(N) satisfies the following: N-1 1 R(N) :> R(i) N . i=1 Hint: R(N) is the probability of the event. How can you break it down into smaller, more tractable probabilities?

A First Course in Probability (10th Edition)
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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B. I really need help! Thanks!

On a Saturday, a hundred students have ordered tacos and they are ready to be picked up. Everyone has ordered different tacos and they are all clearly labeled. The students file in a line one at a time to pick up their orders. Unfortunately, you are the last one on line. However, the first student in line randomly picks from the pile of tacos instead of grabbing their order. As the students come in, if their order is there, they take it; but if it isn't there, they grab a random order. Then, you wonder: what is the probability that you are going to get your tacos without it being taken by another student? Let's consider this situation in the following way: N students line up for their tacos, and you are the last in line. The first student grabs a taco at random, and every student afterwards either takes their own taco or grabs one randomly. Define R(N) to be the probability that you get your own taco in this situation.
Transcribed Image Text:On a Saturday, a hundred students have ordered tacos and they are ready to be picked up. Everyone has ordered different tacos and they are all clearly labeled. The students file in a line one at a time to pick up their orders. Unfortunately, you are the last one on line. However, the first student in line randomly picks from the pile of tacos instead of grabbing their order. As the students come in, if their order is there, they take it; but if it isn't there, they grab a random order. Then, you wonder: what is the probability that you are going to get your tacos without it being taken by another student? Let's consider this situation in the following way: N students line up for their tacos, and you are the last in line. The first student grabs a taco at random, and every student afterwards either takes their own taco or grabs one randomly. Define R(N) to be the probability that you get your own taco in this situation.
3. Show that for N > 2, R(N) satisfies the following: N-1 1 R(N) :> R(i) N . i=1 Hint: R(N) is the probability of the event. How can you break it down into smaller, more tractable probabilities?
Transcribed Image Text:3. Show that for N > 2, R(N) satisfies the following: N-1 1 R(N) :> R(i) N . i=1 Hint: R(N) is the probability of the event. How can you break it down into smaller, more tractable probabilities?
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