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Math Help - Binomial Distribution, balls and questions

  1. #1
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    Binomial Distribution, balls and questions

    I have 2, two part questions.

    1. A box contains 3 yellow and 5 black balls. A ball is drawn and then replaced. This process is continued for a total of 5 draws. what is the probability of drawing:
    a. exactly 4 black balls
    b. at most 4 black balls

    2. A test contains 20 multiple choice questions each with 3 choices. If a student guesses every answer, what is the probability he will get:
    a. all the answers wrong
    b. exactly 5 correct answers.

    Thanks
    ~G
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  2. #2
    Eater of Worlds
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    1. A box contains 3 yellow and 5 black balls. A ball is drawn and then replaced. This process is continued for a total of 5 draws. what is the probability of drawing:
    a. exactly 4 black balls
    C(5,4)(\frac{5}{8})^{4}(\frac{3}{8})^{1}

    b. at most 4 black balls
    EDIT: thanks to Janes cognizance. I fix. See later post.


    2. A test contains 20 multiple choice questions each with 3 choices. If a student guesses every answer, what is the probability he will get:
    a. all the answers wrong
    (\frac{2}{3})^{20}

    b. exactly 5 correct answers.
    C(20,5)(\frac{1}{3})^{5}(\frac{2}{3})^{15}

    Thanks
    ~G[/quote]
    Last edited by galactus; December 24th 2007 at 04:38 PM.
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  3. #3
    Senior Member JaneBennet's Avatar
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    Quote Originally Posted by galactus View Post
    Subtract the above solution from 1.
    Itís actually 1 − P(exactly 5 black) − P(exactly 6 black) − P(exactly 7 black) − P(exactly 8 black).
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  4. #4
    Eater of Worlds
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    But there are only 5 blacks altogether. Nonetheless, I had a brain fart. I was thinking of the 'at least one' case.

    \sum_{k=0}^{4}C(5,k)(\frac{5}{8})^{k}(\frac{3}{8})  ^{5-k}=\frac{29643}{32768}\approx{.9046}

    or

    1-(\frac{5}{8})^{5}= \frac{29643}{32768}\approx{.9046}
    Last edited by galactus; December 24th 2007 at 05:25 PM.
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  5. #5
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    thanks

    I really appreciate both of you taking the time to help me.
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