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Math Help - Probability of students passing med school

  1. #1
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    Red face Probability of students passing med school

    I worked out the following problems though i'm not 100% sure that i've figured them correctly.

    62. at Med University, the failure rate is 0.2 per year. There are 15 students registered in the first-year class. Give all your answers correct to 4 decimal places.
    a. what is the probability that all of them will pass?
    b. what is the probability that exactly 12 of them will pass?
    c. what is the probability that at least 12 of them will pass?

    a. p = 0.2^0(1-0.2)^15
    = 0.8^15
    = 0.0352

    therefore the probability of all of them passing is 0.0352 or 3.52%

    b. p = 0.2^12(1-0.2)^15-12
    = 0.000000004(0.8)^3
    = 0.000000004(0.512)
    = 0.000000002

    therefore, the probability of exactly 12 of them passing is 0.000000002

    c. p1 = 0.000000002
    p2 = 0.2^13(1-0.2)^15-13
    = 5.243x10^-10
    p3 = 0.2^14(1-0.2)^15-14
    = 1.311x10^-10
    p4 = 0.0352
    now for this question i'm not too sure where to head from here to get the finaly probabilty and not to have 4 separate probabilities.
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  2. #2
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    Quote Originally Posted by lexx View Post
    I worked out the following problems though i'm not 100% sure that i've figured them correctly.

    62. at Med University, the failure rate is 0.2 per year. There are 15 students registered in the first-year class. Give all your answers correct to 4 decimal places.
    a. what is the probability that all of them will pass?
    b. what is the probability that exactly 12 of them will pass?
    c. what is the probability that at least 12 of them will pass?

    a. p = 0.2^0(1-0.2)^15
    = 0.8^15
    = 0.0352

    therefore the probability of all of them passing is 0.0352 or 3.52%

    b. p = 0.2^12(1-0.2)^15-12
    = 0.000000004(0.8)^3
    = 0.000000004(0.512)
    = 0.000000002

    therefore, the probability of exactly 12 of them passing is 0.000000002

    c. p1 = 0.000000002
    p2 = 0.2^13(1-0.2)^15-13
    = 5.243x10^-10
    p3 = 0.2^14(1-0.2)^15-14
    = 1.311x10^-10
    p4 = 0.0352
    now for this question i'm not too sure where to head from here to get the finaly probabilty and not to have 4 separate probabilities.
    By "failure rate is 0.2" do you mean that the probability of failing is 0.2? If yes, then your calculations look OK. In the calculation for (c) you have to add the probabilities together.
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  3. #3
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    yes the failure rate is also the probability of students failing each year. thank you for your help with these questions.
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