Question 1072486: In a certain college, 33% of the physics majors belong to ethnic minorities. If 8 students are selected at random from the physics majors, what is the probability that more than 5 belong to an ethnic minority?
0.0659
0.9154
0.0187
0.0846
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this looks like a binomial probability type problem.
the formula is:
p(x) = p^x * q^(n-x) * c(n,x)
p is the probability that a student is a minority.
this makes p = .33
q is the probability that a student is not a minority.
this makes q = 1 - .33 = .67
c(n,x) is the number of ways you can get x minority students out of n students.
n is the total number of students.
you have n = 8, p = .33 and q = .67
c(n,x) is equal to n! / (x! * (n-x)!)
you want to know the probability that more than 5 out of the 8 students will be a minority.
this means you want to know the probability that 6 or 7 or 8 students out of 8 students is a minority.
using the formula of p(x) = p^x * q^(n-x) * c(n,x), then you want the sum of:
p(6) + p(7) + p(8)
p(6) = .33^6 * .67^2 * c(8,6)
p(7) = .33^7 * .67^1 * c(8,7)
p(8) = .33^8 * .67^0 * c(8,8)
c(8,6) = 8! / (6! * 2!) = 56/2 = 28
c(8,7) = 8! / (7! * 1!) = 8
c(8,8) = 8! / (8! * 0!) = 1
formulas become:
p(6) = .33^6 * .67^2 * 28 = .016233
p(7) = .33^7 * .67^1 * 8 = .00228
p(8) = .33^8 * .67^0 * 1 = .00014
add these up and round to the 4th decimal place and you get:
p(6) + p(7) + p(8) = .0187
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