SOLUTION: Please help me find the answer to this question: Recent information published by the U.S. Environmental Protection Agency indicates that Honda is the manufacturer of four of the t

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Question 872753: Please help me find the answer to this question:
Recent information published by the U.S. Environmental Protection Agency indicates that Honda is the manufacturer of four of the top nine vehicles in terms of fuel economy. a. Determine the probability distribution for the number of Hondas in a sample of three cars chosen from the top nine. b. What is the likelihood that in the sample of three at least one Honda is included?
I was trying to use this formula P (X) = nCx @^x(1-@)^n-x (@ is the probability of a success on each trial)
P(x=0) = 3C0 (5/9)^0 (1-5/9)^3-0 = (1)(1)(.171467) = .171467 no Hondas
P (x=1) = 3C1 (5/9)^1 (1-5/9)^3-1 = (.05) (.5556) (.6914) = .0192 for 1 Honda
P (x=2) = 3C2 (5/9) ^2 (1-5/9)^ 3-2 = (3) (.3086) (.4444) = .4114 for 2 Hondas
P (x=3) =3C3 (5/9)^3 (1-5/9)^3-3 =(.1667) (.1715) (I'm stuck)
What am I doing wrong?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Recent information published by the U.S. Environmental Protection Agency indicates that Honda is the manufacturer of four of the top nine vehicles in terms of fuel economy.
P(honda) = 4/9
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a. Determine the probability distribution for the number of Hondas in a sample of three cars chosen from the top nine.
Binomial Problem with n = 3 and p(H) = 4/9
mean = np = 3(4/9( = 4/3
std = sqrt(npq) = sqrt((4/3)(5/9)) = sqrt(20/27) = (2/3)sqrt(5/3)
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b. What is the likelihood that in the sample of three at least one Honda is included?
P(at least 1) = 1 - P(none)
P(at least 1) = 1 - (5/9)^3 = 0.8285
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Cheers,
Stan H.