Probability of a restaurant accomodating everybody

[duki]

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

 

[sylas]

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

 

[duki]

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)

 

[diazona]

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?

 

[duki]

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

 

[diazona]

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?

 

[duki]

51 and 52

 

[sylas]

51 and 52

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

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