SOLUTION: Ok tried this Three times and get figure out how to get the answer. 37% of all doctors are family practioners. If there are 5 doctors at a gathering, what is the probability tha

Question 789037: Ok tried this Three times and get figure out how to get the answer.
37% of all doctors are family practioners. If there are 5 doctors at a gathering, what is the probability that 3 of them are family practioners?
I am 53 years of age, out of school since the 70's - never had to do Formulas and am completely confused (I am back in college earning my Bachelors in Liberal Arts) I am failing Statistics because I do not understand it. Can someone PLEASE help?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let's say we have 100 doctors, then 37% of 100 gives us 37 doctors that are family practitioners
then we are told that at a gathering we have 5 doctors and to calculate the probability that 3 of them are family practitioners
now we use combinations to calculate the probability
we multiply the combination of 37 taken 3 at a time by the combination of 63 taken two at a time and then divide by the combination of 100 taken 5 at a time
the combination of 37 taken 3 at a time = 37! / (3! * (37-3)!) = 7770
the combination of 63 taken two at a time = 1953
the combination of 100 taken 5 at a time = 7.528752e7
now we can calculate
(7770 * 1953) / 7.528752e7
1.517481e7 / 7.528752e7
0.20155810684161199625
this tells us that the probability that 3 doctors are family practitioners is 20%

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