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Math Help - Stumped on how to answer multi step probability question.

  1. #1
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    Stumped on how to answer multi step probability question.

    Hey, I don't know where to start with this question.

    Question:
    On a multiple-choice test of 10 questions, each question has 5 possible answers. A student is certain of the answers to 4 questions but is totally baffled by 6 questions. If the student randomly guesses the answers to those 6 questions, what is the probability that the student will get a score of 5 or more on the test? Express your answer correct to two decimal places.

    Solution
    Okay, so I am assuming that the 4 questions the student is certain about are guaranteed to be correct. That leaves the other 6. All I really need to find here is the probability of getting all 6 questions incorrect. So I believe that would be:
     (\frac{5}{4}) (\frac{5}{4}) (\frac{5}{4}) (\frac{5}{4}) (\frac{5}{4}) (\frac{5}{4}) which gives me:  \frac{4096}{15625} .
    So to find the probability that the student will get a score of 5 or more on the test is  1 - \frac{4096}{15625} which gives an answer of:  0.737856 (my calculator for some reason put it into decimal form -.-).

    Did I do this question correctly? I actually originally had very little on this question at all, and as I was writing this out this solution came to me. Does this solution make sense?

    - Thanks!
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  2. #2
    MHF Contributor
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    Yeah, that's it (apart from writing the 0.8 fraction upside-down of course! and you didn't express the final answer to two decimal places)
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  3. #3
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    Haha! Whoops, I didn't even realize I did that. Thank you for confirming my answer!
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