Probability of a restaurant accomodating everybody

Is that the probability that the restaurant will be able to accommodate everyone?No, that's the probability that all 52 reservations will show up. To find the probability that the restaurant will be able to accommodate everyone, we need to find the probability that there will be 0 reservations that don't show up. And that probability is 0.8^0, which is equal to 1. Therefore, the probability that the restaurant will be able to accommodate everyone is 1 - 0.8^0 = 1 - 1 = 0In summary, the probability that the restaurant will be able to accommodate everyone is 0.
  • #1
duki
264
0

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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  • #2


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
 
  • #3


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)
 
  • #4


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?
 
  • #5


20% that they don't and 80% that they do?
 
  • #6


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?
 
  • #7


51 and 52
 
  • #8


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?
 

Related to Probability of a restaurant accomodating everybody

1. What is the probability of a restaurant being able to accommodate everyone in a large group?

The probability of a restaurant being able to accommodate a large group depends on several factors, such as the size of the group, the availability of tables and seating, and the restaurant's current reservations. It is difficult to determine an exact probability, but restaurants typically try to accommodate as many customers as possible.

2. How does the size of a group affect the probability of a restaurant accommodating everyone?

The size of a group can greatly impact the probability of a restaurant accommodating everyone. Larger groups may require more tables and seating, which can be limited in some restaurants. Additionally, larger groups may also require more time and resources from the restaurant staff, so the availability of reservations may also play a role.

3. Can a restaurant guarantee that they will be able to accommodate everyone in a group?

Unfortunately, no restaurant can guarantee that they will be able to accommodate everyone in a large group. As mentioned before, there are several factors that can affect the probability of accommodating a group, and these factors are constantly changing. It is always best to call the restaurant in advance to discuss accommodations for a large group.

4. What can I do to increase the chances of a restaurant accommodating my group?

If you are planning to dine with a large group, it is best to make a reservation in advance. This will give the restaurant time to prepare and potentially make accommodations for your group. It is also helpful to call and discuss your group's needs with the restaurant beforehand, so they can better plan for your arrival.

5. Is there a way to calculate the exact probability of a restaurant accommodating everyone in a group?

As mentioned before, it is difficult to calculate the exact probability of a restaurant accommodating a group. This is because there are many variables that can affect the probability, such as the size of the group, the availability of tables and reservations, and the restaurant's current capacity. The best way to ensure accommodation for a group is to make a reservation and communicate with the restaurant beforehand.

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