Question

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)?

Answer 1

0.71

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