SOLUTION: the working women executive magazine reports that 65% of all new female car buyers are women. Assuming that those figures are correct; find the probability that if we select six w

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Question 602512: the working women executive magazine reports that 65% of all new female car buyers are women. Assuming that those figures are correct; find the probability that if we select six women at random that four women will be new car buyers
Compute the probability by solving the binomial distribution formula the long way by hand.
Answer by jim_thompson5910(35256) About Me  (Show Source):
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P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x)

P(X = 4) = (6 C 4)*(0.65)^(4)*(1-0.65)^(6-4)

P(X = 4) = (6 C 4)*(0.65)^(4)*(0.35)^(6-4)

P(X = 4) = (15)*(0.65)^(4)*(0.35)^2

P(X = 4) = (15)*(0.17850625)*(0.1225)

P(X = 4) = 0.328005234375