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8 June, 18:03

In a certain college class, 40% of the admitted students were in top 10% of their high school class, 25% were in the next 10%, and the remaining 35% were below the top 20%. Of these students, 90%, 70%, and 20% were passing this course, respectively. If a randomly selected student is failing, then what is the probability that this student was below 20% of his or her high school class (round off to second decimal place) ?

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  1. 8 June, 18:09
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    0.71

    Step-by-step explanation:

    The fraction of students failing is the sum of the fractions of students failing in each category. Those fractions are ...

    top 10%: 0.40 * (1 - 0.90) = 0.04

    next 10%: 0.25 * (1 - 0.70) =.075

    bottom 80%: 0.35 * (1 - 0.20) = 0.28

    So, the total fraction of students failing is ...

    0.04 + 0.075 + 0.28 = 0.395

    The desired probability is ...

    p (bottom 80% | failing) = p (bottom 80% & failing) / p (failing)

    = 0.28/0.395 ≈ 0.7089 ≈ 0.71
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