5 patients in 30 days, Dr P called 5 times in 30 days; find

Out of 30 days in a month - the number of times a patient will come into the emergency room with a broken arm is 5.

Out of 30 days in a month, Dr. Payne is on call to treat broken arms 5 days.

What is the probability that Dr. Payne will treat 1 patient with a broken arm in 30 days, if he is on call 5 days in a month.

Thanks,
Katie

Re: Statistics Question

Since the doctor is only in 5 days out of 30, the probability he is on call is 5/30=1/6.

We can use a binomial probability: \(\displaystyle C(n,k)p^{k}q^{n-k}\)

where k=1, p=1/6, q=1-p, n=5

So, we have:

\(\displaystyle 5\cdot (\frac{1}{6})\cdot (\frac{5}{6})^{4}\)