Probability/Statistics

A quiz consists of 10 multiple-choice questions, each with 4 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 70 %.

I'm not sure what to do. I figured that there's 10 questions, each with a 1/4 chance. I took 10*1/4=2.5 and multiplied that by .70, but my answer wasn't right. What am I missing?

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  1. To pass he must guess
    1. exactly 7 out 10 or
    2. exactly 8 out 10 or
    3. exactly 9out 10 or
    4. exactly 10 out 10

    prob of exactly 7 out 10 = C(10,7)(1/4)^7(3/4)3 = 120(1/16384)(27/64) = .00309
    prob of exactly 8 out 10 = C(10,8)(1/4)^8(3/4)^2 = .000386
    prob of exactly 9 out 10 = C(10,9)(1/4)^9(3/4) = .000018
    prob of exactly 10 out 10 = C(10,10)(1/4)^10 = .00000095

    for a total of .0035055 as the probability.

    suggestion: study, and don't guess

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