# Binomial Distribution Prob: Desks needed to serve grad TAs 90% of time?

#### Raj1234

##### New member
I am new to probability and using One of the books to learn the concepts. I got stuck in following problem.
The mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just as likely to study at home as in the office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?
Probability of each student being in office is 1/2. So probability of all 8 in office is 1/256, similarly 7 in office is 8/256 etc. But I am not able to link these information with the question of how many desks.
Any guidance will be highly appreciated.

#### Dr.Peterson

##### Elite Member
I am new to probability and using One of the books to learn the concepts. I got stuck in following problem.
The mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just as likely to study at home as in the office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?
Probability of each student being in office is 1/2. So probability of all 8 in office is 1/256, similarly 7 in office is 8/256 etc. But I am not able to link these information with the question of how many desks.
Any guidance will be highly appreciated.
I think you have the probability part clear; it's just interpreting the problem!

Suppose there are 8 desks. What is the probability that everyone has a desk? 100%, right? That's at least 90%; but what we want is the LEAST number of desks for which this is true.

Suppose there are 7 desks. Now what is the probability that everyone has a desk? It's the probability that 7 or fewer are in the office -- that is, 1 minus the probability that all 8 are in the office. What is this probability?

If that is at least 0.90, then the answer is 7 desks. If it is lower, then move on to the next number.

Once you've finished this process, you'll be able to describe a specific strategy you could have used; but there's nothing wrong with learning what a problem is asking bit by bit, by asking questions like these.

#### Raj1234

##### New member
I think you have the probability part clear; it's just interpreting the problem!

Suppose there are 8 desks. What is the probability that everyone has a desk? 100%, right? That's at least 90%; but what we want is the LEAST number of desks for which this is true.

Suppose there are 7 desks. Now what is the probability that everyone has a desk? It's the probability that 7 or fewer are in the office -- that is, 1 minus the probability that all 8 are in the office. What is this probability?

If that is at least 0.90, then the answer is 7 desks. If it is lower, then move on to the next number.

Once you've finished this process, you'll be able to describe a specific strategy you could have used; but there's nothing wrong with learning what a problem is asking bit by bit, by asking questions like these.
Thank you Dr.Peterson. Your answer makes the concept clear to me.