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Math Help - how would i calculate these probabilities, if i'm not given success...?

  1. #1
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    how would i calculate these probabilities, if i'm not given success...?

    the problem is as follows: "a student didn't study for a 20 question quiz which has 5 possible answers, and therefore will guess on every question. find each probability-prob. the student gets at least 50% on test, prob. student gets at most 75% on test, and prob. student gets at least a 70% on the test."


    well, i know prob right=1/5 and prob wrong= 4/5. so, when setting up my prob. for each part, would pi be .2 because that's success right?
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  2. #2
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    The probability the student gets at least a 50% means the student must get at least 10 out of the 20 correct.

    The prob. of getting a problem correct is 1/5. Therefore, binomial

    at least 50%

    \sum_{k=10}^{20}C(20,k)(\frac{1}{5})^{k}(\frac{4}{  5})^{20-k}

    The others are analogous to this one.


    At most 75%:

    \sum_{k=0}^{15}C(20,k)(\frac{1}{5})^{k}(\frac{4}{5  })^{20-k}


    at least 70%:

    \sum_{k=14}^{20}C(20,k)(\frac{1}{5})^{k}(\frac{4}{  5})^{20-k}
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