Question 933536: A financial magazine was asked to obtain a list of 10 randomly selected upper management
personnel in Canada. If 15% of upper management are women
What is the probability that there are 6 men’s names on the list?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! probability of being a woman is .15
probability of being a man is .85
the binomial probability equation is p(x) = c(n,x) * p^x * q^(n-x)
n = 10
x = 6
n-x = 4
formula becomes:
p(6) = c(10,6) * .85^6 * .15^4 which becomes:
p(6) = 210 * .85^6 * .15^4 which becomes:
p(6) = .04 rounded to 2 decimal places.
c(n,x) is the combination formula of n! / (x! * (n-x)!)
when n = 10 and x = 6, the formula becomes:
c(10,6) = 10! / (6! * 4!) = (10*9*8*7*6!) / (6! * 4!)
the 6! in the numerator and the 6! in the denominator cancel out and you are left with:
c(10,6) = (10*9*8*7) / (4*3*2*1).
the 8 in the numerator and the 4*2 in the denominator cancel out.
the 9 in the numerator and the 3 in the denominator becomes 3 in the numerator.
you are left with:
c(10,6) = 10*3*7 which is equal to 210.
your solution is .04 rounded to 2 decimal places.
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