Question 48

At a college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidates who are really capable, 80% pass the tests and of the incapable, 25% pass the tests. Given that 40% of the candidates are really capable, then the proportion of capable college students who passed is about

Solution

Let the total candidates = t and capable candidates be x and incapable be y.

Passing the tests = 0.8x + 0.25y

Fail the test = 0.2x + 0.75y

Given x = 40/100*t and y = 0.6t

Pass = 0.8*0.4t + 0.25*0.6t = 0.32t + 0.15t = 0.47t

Proportion of capable college students who passed is = 32/47 = 68%

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