statistics

you have 8 blue marbles, 7 red marbles, and 5 green marbles. What is the probability of obtaining at least 2 red marbles in three draws with replacements?

I have the answer, just can't figure out how to get it.

Thanks!

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  1. Seven out of the twenty are red. The probability of NOT getting ANY red in three tries is (13/20)^3 = 0.2746
    The probability of getting only one red is 3*(13/20)^2*(7/20) = 0.4436
    The probability of getting two or more is 1 - 0.2736 - 0.4436 = 0.2828

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  2. I thought I was understanding this but I am really not sure about the symbols.
    Does the 3*(13/20)^2*(7/20) translate to 3 times 13/20 times 2 times 7/20?
    Sorry I am not up on the symbols...
    I will keep trying.

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  3. 3*(13/20)^2*(7/20)
    means
    three times (13/20) squared times (7/20)
    in general the probability of getting r successes out of n tries in binomial distribution if probability of success is p is
    P(r) = C(n,r) p(r)^r (1-p)^(n-r)

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  4. That is even more confusing. I am totally lost on this problem.
    I know that I have to multiply the three possibilities, so (7/20)(7/20)(13/20) three times (same numbers, different order) and I get 0.07963. I thought I would add those three numbers or essentially multiply that number by three, however, I did not get the right answer doing it that way.

    Thanks for any help. I am totally confused.

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