N-1 1 R(N) = - - N2 R(i) i=1 Hint: R(N) is the probability of the event. How can you break it down into smaller, more tractable probabilities? 1. Suppose that at the start, the taco maker puts out an extra taco. So, anyone grabbing a random taco might grab it instead of someone else's. Let X(N) be the probability that you get your taco. What is X(2)? 2. If applicable, repeat the analysis. What is X(100)?
N-1 1 R(N) = - - N2 R(i) i=1 Hint: R(N) is the probability of the event. How can you break it down into smaller, more tractable probabilities? 1. Suppose that at the start, the taco maker puts out an extra taco. So, anyone grabbing a random taco might grab it instead of someone else's. Let X(N) be the probability that you get your taco. What is X(2)? 2. If applicable, repeat the analysis. What is X(100)?
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fbff82e-583d-4003-b329-07736a7bbd92%2F0abb09c7-c0fe-4469-af9d-a67533851a9a%2F66ouvxd_processed.png&w=3840&q=75)
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.
![N-1
1
R(N) =
- -
N2 R(i)
i=1
Hint: R(N) is the probability of the event. How can you break it down into smaller, more
tractable probabilities?
1. Suppose that at the start, the taco maker puts out an extra taco. So, anyone grabbing a
random taco might grab it instead of someone else's. Let X(N) be the probability that
you get your taco. What is X(2)?
2. If applicable, repeat the analysis. What is X(100)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fbff82e-583d-4003-b329-07736a7bbd92%2F0abb09c7-c0fe-4469-af9d-a67533851a9a%2Fucpprg_processed.png&w=3840&q=75)
Transcribed Image Text:N-1
1
R(N) =
- -
N2 R(i)
i=1
Hint: R(N) is the probability of the event. How can you break it down into smaller, more
tractable probabilities?
1. Suppose that at the start, the taco maker puts out an extra taco. So, anyone grabbing a
random taco might grab it instead of someone else's. Let X(N) be the probability that
you get your taco. What is X(2)?
2. If applicable, repeat the analysis. What is X(100)?
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