Answer :

Let X be the number of a graduate assistants.


X = 8


Let p be the probability of the assistant studying at the office.


Then, q be the probability of the assistant studying at home.


According to the question, each assistant is just likely to study at home as in the office.



Also, we know that (p + q) = 1.


q = 1 – p





Now, let there be k number of desks in the office.


We need to find the number of desks in the office so that each assistant has a desk at least 90% of the time.






P (X > k) < 0.10


Now, we must find a value of k that satisfies the above equation.


Clearly,


P (X > 5) = P (X = 6 or X = 7 or X = 8)












P (X > 5) = 0.14


Also, P (X > 6) = P (X = 7 or X = 8)










P (X > 6) = 0.035


, P (X > 6) < 0.10


Hence, if there are 6 desks, then there is atleast 90% chance for every graduate assistant to get a desk.


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