SOLUTION: Here is a question I can't figure out how to get started. I considered using the binomial formula but it looks like it would take ages to calculate, I must be missing the point!

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Question 578753: Here is a question I can't figure out how to get started. I considered using the binomial formula but it looks like it would take ages to calculate, I must be missing the point!
Past car sales experience has shown that 22% of all luxury cars sold are black. If 45 recent sales of luxury cars are randomly selected. Find the following probabilities:
1. At least 2 cars are black.
2. Exactly 6 are black. (I attempted this one using the binomial prob. formula and got 8.9417
3. Between 1 and 4 cars (inclusive) are black.
4. No more than 3 cars are black.
5. More than 40 cars are not black.
Guessing I have to begin with n, x, p and q.
Thanks for the guidance.
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
yes, you have to sum a few terms of the expansion (it shouldn't take "ages")

the expansion is ___ (Pb + Pn)^45 ___ (.22 + .78)^45

1. 43 (or less) are not black
___ subtracting the last 3 terms from one ___ 1 - {[(.78)^45] + 45[.22 (.78)^44] + 990[(.22)^2 (.78)^43]}

2. 45C6 [(.22)^6 (.78)^39] = .0572 (approx)

3. sum those four terms

4. see #1 ___ 42 (or more) are not black

5. see #3 ___ 4 (or less) are black