Probability of a restaurant accomodating everybody

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Homework Help Overview

The problem involves calculating the probability of a restaurant being able to accommodate all reservations given that a certain percentage of people do not show up. The context includes a restaurant with 50 tables and 52 reservations, with a known no-show rate of 20%.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the probability of no-shows and explore the implications of independent events. There is mention of using a probability distribution to model the situation, with questions about specific probabilities and the concept of distributions.

Discussion Status

Participants are actively engaging with the problem, questioning assumptions about probabilities and discussing the nature of the distribution needed. Some guidance has been provided regarding the probability of individual reservations showing up or not, and the implications for the total number of attendees.

Contextual Notes

There is a lack of familiarity with probability distributions among some participants, which may affect their ability to fully engage with the problem. The independence of events is noted as an assumption that is necessary for the calculations.

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Homework Statement



experience shows that 20% of the people reserving tables at a certain restaurant never show up. If the restaurant has 50 tables and takes 52 reservations, what is the probability that it will be able to accommodate everyone?

Homework Equations



The Attempt at a Solution



I'm not really sure where to begin... I tried starting out saying of 50 tables there is a 80% chance that only 40 tables would be filled... but I have no idea
 
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duki said:

Homework Statement



experience shows that 20% of the people reserving tables at a certain restaurant never show up. If the restaurant has 50 tables and takes 52 reservations, what is the probability that it will be able to accommodate everyone?

Homework Equations



The Attempt at a Solution



I'm not really sure where to begin... I tried starting out saying of 50 tables there is a 80% chance that only 40 tables would be filled... but I have no idea

You have 52 reservations, and each one has a probability of 20% of not showing up. (You should also assume these are independent events, which is not explicit in the problem statement, but is needed for a solution).

You should be able to have a probability distribution, with probabilities for n=0, n=1, n=2 and so on all the way up to n=52; where n is the number of reservations that don't show up. Do you know what distribution to use for this? That would give you relevant equations.

Can you calculate, for example, the probability that exactly one reservation doesn't show up?

Cheers -- sylas
 


Thanks for the reply!
Actually I have no idea what a distribution is... I'm completely new to this stuff. The only thing I'm semi-familiar with is building the trees (like in the case of flipping coins multiple times)
 


In that case, the first thing to think about is: if you pick out one particular reservation, what's the probability that that person does not show up? And what's the probability that the person does show up?
 


20% that they don't and 80% that they do?
 


OK, good. Now, let's say that n is the number of people that do show up. What are the possible values for n for which the restaurant will not be able to accommodate everyone?
 


51 and 52
 


duki said:
51 and 52

*Tag* ... I'm back to take up the Q&A session for a bit. :wink:

Very good! Now... what is the probability that all 52 reservations show up?
 

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