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Math Help - Bernoulli/Binomial Distributions

  1. #1
    Rhymes with Orange Chris L T521's Avatar
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    Bernoulli/Binomial Distributions

    There is this one part of a problem I'm having trouble setting up...

    On a six-question multiple-choice test there are five possible answers for each question, of which one is correct (C) and four are incorrect (I). If a student guesses randomly and independently, find the probability of
    For this, I let X=1 if answer is correct, and X=0 if the answer is incorrect.

    (a) Being correct only on questions 1 and 4 (i.e. C, I, I, C, I, I)
    I'm not quite sure on how to set this part up, any hints would be appreciated.

    (b) Being correct on two questions
    I think this would be P\left(X=2\right)=\binom62\left(\frac{1}{5}\right)  ^2\left(\frac{4}{5}\right)^4...but I'm not quite sure.

    I'd appreciate any input!

    --Chris
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    There is this one part of a problem I'm having trouble setting up...

    On a six-question multiple-choice test there are five possible answers for each question, of which one is correct (C) and four are incorrect (I). If a student guesses randomly and independently, find the probability of

    (a) Being correct only on questions 1 and 4 (i.e. C, I, I, C, I, I)

    For this, I let X=1 if answer is correct, and X=0 if the answer is incorrect.

    I'm not quite sure on how to set this part up, any hints would be appreciated.

    (b) Being correct on two questions
    I think this would be P\left(X=2\right)=\binom62\left(\frac{1}{5}\right)  ^2\left(\frac{4}{5}\right)^4...but I'm not quite sure.

    I'd appreciate any input!

    --Chris
    (b) is correct.

    For (a), it's simply  \left( \frac{1}{5}\right) \, \left( \frac{4}{5}\right)^2 \, \left( \frac{1}{5}\right) \, \left( \frac{4}{5}\right)^2 = \left( \frac{1}{5}\right)^2 \, \left( \frac{4}{5}\right)^4.
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