SOLUTION: What type of problem is this and how do I solve it? If 15 of the students from the special programs are randomly selected, find the probability that 12 of them graduated (84% fo

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Question 1130879: What type of problem is this and how do I solve it?
If 15 of the students from the special programs are randomly selected, find the probability that 12 of them graduated (84% for students admitted through special programs).
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
15 students from the special program are selected.
84.
the probability that a student from the special program graduates is 84% = .84
you want to find the probability that 12 of them graduated.

looks like a binomial probability type problem.

equation for that is p(x) = p^x * q^(n-x) * c(n,x)

in this problem, that becomes:

p(12) = .84 ^ 12 * (1 - .84) ^ 15 - 12) * c(15,12)

.84 is the probability that a student from the special program will graduate.
1 - .84 = .16 is the probability that a student from the special program will not graduate.
c(15,12) = the number of ways you can get a set of 12 elements from a set of 15 elements = 15! / (12! * 3!) = 455

the formula becomes .84 ^ 12 * .16 ^ 3 * 455 = .229997321.

i checked out all the probabilities using excel.
the total probability is 1 as it should be.
here's a display of what excel showed me.

$$$

look at the row where x = 12 and you'll see that p(x) equals 0.229997321 which is the same as i got manually using my scientific calculator.

that is the probability that exactly 12 of them graduated if you picked those 12 out of 15 randomly selected student in the special program.