SOLUTION: Nine customers at a supermarket are asked if they use brand X laundry soap. In general, 22% of the population use this brand. What is the probability that among the nine, more tha

Question 254875: Nine customers at a supermarket are asked if they use brand X laundry soap. In general, 22% of the population use this brand. What is the probability that among the nine, more than two people use brand X? (round answer to 4 decimal places).
I keep getting impossible answers so I'm not sure if I'm setting the problem up wrong, or calculating it wrong.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
this is a binomial expansion problem
people either use (U with probability .22) or don't use (D with probability .78)

you need the sum of the first seven terms of the expansion (U + D)^9

it is easier to sum the last three terms and subtract from 1

1 - [36(U^2 D^7) + 9(U D^8) + (D^9)]

1 - [36(.22^2 * .78^7) + 9(.22 * .78^8) + (.78^9)]
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