SOLUTION: An event E has a probability p = p(E) = 0.3 in some sample space. Suppose the experiment that yields this sample space is repeated six times and the outcomes are independent. Find

Question 515045: An event E has a probability p = p(E) = 0.3 in some sample space. Suppose the experiment that yields this sample space is repeated six times and the outcomes are independent. Find the probability of getting the following outcome. (Round your answer to six decimal places.)
E exactly two times
i did C(6,2)(.3)^2(1-.3)=.945, but it wasnt right. Please help
Answer by drcole(72) (Show Source): You can put this solution on YOUR website!
You almost have the right answer. This is an example of a binomial distribution problem. If an experiment can only have two outcomes (usually written "success" and "failure," but in this case E and "not E"), the probability of success (in this case E) is p, the probability of failure (in this case "not E") is q = 1 - p, and the experiment is repeated N times with the outcomes of each experiment being independent of each other, then the probability of exactly k success (and thus N - k failures) is:
P(k successes) =
In this case, N = 6, k = 2, N - k = 4, p = 0.3, and q = 1 - 0.3 = 0.7. So we substitute into the formula:
P(k successes) =
So your only mistake is leaving off the exponent on 0.7.
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