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Math Help - Combinatorics & Binomial Probability

  1. #1
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    Combinatorics & Binomial Probability

    Hi all, I'm having troubles figuring out how to answer these questions and similar questions.


    Combinatorics
    In the long run 40% of patients treated for a particular disease with the drug streptomycin are cured. If a doctor were to treat 10 randomly chosen patients with the drug, what is the probability of:
    i) 6 cures
    ii) more than 8 cures?


    A second doctor treats 10 patients with a new treatment and obtains 6 cures. Comment on this result.


    And


    A management team consists of 12 people. In how many ways could a sub-committee of 4 people be formed?


    Thirty-two students are to be interviewed for 8 different jobs. In how many ways could the jobs be filled by selecting from these applicants.

    Binomial Probability


    A printer which has been giving trouble produces an error message on 3 out of every 10 print jobs on average.



    What is the probability of this printer successfully doing 4 print jobs in a row?


    Find the probability of drawing 2 red tokens from a box containing 5 red, 3 white and 5 yellow tokens. The tokens are drawn one at a time without replacement?


    Thanks a lot.
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  2. #2
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    Re: Combinatorics & Binomial Probability

    Quote Originally Posted by Jaytohkay View Post
    In the long run 40% of patients treated for a particular disease with the drug streptomycin are cured. If a doctor were to treat 10 randomly chosen patients with the drug, what is the probability of:
    i) 6 cures
    ii) more than 8 cures?
    Apply the fact that \displaystyle P(x=k) = \binom{n}{k}\times p^k\times (1-p)^{n-k}

    You have p = 0.4 and n=10

    find

    P(x=6)

    and

    P(x\geq 8) = P(x= 8)+P(x=9)+P(x=10)
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  3. #3
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    Re: Combinatorics & Binomial Probability

    Thanks for the help, but I don't understand those formulas or how to use them, could you please explain a bit more as I'm having trouble interpreting them.
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  4. #4
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    Re: Combinatorics & Binomial Probability

    Which bit do you not understand?
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  5. #5
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    Re: Combinatorics & Binomial Probability

    Quote Originally Posted by pickslides View Post
    Which bit do you not understand?
    I've never seen a formula like it before as I rarely deal with them at my level of math. So I don't know how to interpret it correctly.

    How I'm seeing the first bit is


    You have p = 0.4 and n=10
    P(.4) = (10/.4(25)

    Then I just don't understand the rest.
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