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2 January, 03:19

If every student is independently late with probability 10%, find the probability that in a class of 30 students: a) nobody is late, 4.2% 8.0% 17.4% 33.3% unanswered b) exactly 1 student is late. 3.33% 5.25% 7.75% 14.1%

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  1. 2 January, 03:25
    0
    a) 4.2%

    b) 14.1%

    Step-by-step explanation:

    a) 0.9³⁰ = 0.0423911583

    b) 30C1 * 0.1 * 0.9²⁹ = 0.1413038609
  2. 2 January, 03:45
    0
    a.) 4.2%

    b.) 14.1%

    Step-by-step explanation:

    We solve using the probability distribution formula for selection and this formula uses the combination formula for estimation.

    When choosing a random selection of "r" items from a sample of "n" items, The formula is generally denoted by:

    P (X=r) = nCr * p^r * q^n-r.

    Where p = probability of success

    q = probability of failure.

    From the given question,

    n = number of samples = 30,

    p = Probability that a student is late = 10% = 0.1,

    q=0.9

    a.) when no student is late, that is when r = 0, then

    P (X=0) = 30C0 * 0.1^0 * 0.9^30

    P (X=0) = 0.0424 = 4.24 ≈ 4.2%

    b.) when exactly one student is late, that is when r=1, then

    P (X=1) = 30C1 * 0.1¹ * 0.9^29

    P (X=1) = 0.1413 = 14.13 ≈ 14.1%
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