SOLUTION: A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% of this population prefers the color green. If 20 buyers are randomly select

Question 1203023: A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40%
of this population prefers the color green. If 20
buyers are randomly selected, what is the probability that exactly a fifth of the buyers would prefer green? Round your answer to four decimal places.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p = .4
q = 1 - .4 = .6
n = 20
p(x) = p^x * q^(n-x) * c(n,x)
when since 1/5 of 20 = 4, the formula becomes:
p(4) = .4^4 * .6^16 * c(20,4) = .03499.
that becomes 3.499% which rounds to 3.5%.

c(n,x) is equal to n! / (x! * (n-x)!)
that becomes 20! / (4! * 16!)
that becoms (20*19*18*17*16!) / (4! * 16!)
that becomes (20*19*18*17) / (4*3*2*1) which is equal to 4845
p(4) becomes equal to .4^4 * .6^16 * 4845 = .03499 rounded to 5 decimal digits.

i calculated the total probabilities in excel.
hare are the results.
the sum of all the proabilities equals 1, as it should.
here are the results.

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