Question

A survey of needy and disabled youths showed that 54% of those who had no preschool education were arrested or charged with a crime by the time they were 19, whereas only 28% who had preschool education wound up in this category. The survey did not specify what percentage of the youths in the survey had preschool education, so let us take a guess at that and estimate that 26% of them had attended preschool. (Round all answers to the nearest 1%.)

(a) What percentage of the youths arrested or charged with a crime had no preschool education?
%

(b) What would this figure be if 74% of the youths had attended preschool?
%

(c) Would youths who had preschool education be more likely to be arrested or charged with a crime than those who did not? Support your answer by quoting probabilities. Select a choice from below.

Choice 1: Youths who did not have preschool education would be more likely to be arrested or charged with a crime than those who did. This claim is supported by the given information: 54% of those who had no preschool education were arrested or charged with a crime, as opposed to only 28% who had preschool education.

Choice 2: Youths who had preschool education would be more likely to be arrested or charged with a crime than those who did not. This claim is supported by the given information: 54% of those who had preschool education were arrested or charged with a crime, as opposed to only 28% who had no preschool education.    

Answer 1

(a) P(arrested) = 0.54*(1-0.26) + 0.28*0.26 = 0.4724

P(no pre school | arrested) = (0.54*0.74)/0.4724 = 85%

(b) P(arrested) = 0.54*(1-0.74) + 0.28*0.74 = 0.3476

P(no pre school | arrested) = (0.54*0.26)/0.3476 = 40%

(c) Choice 1: Youths who did not have preschool education would be more likely to be arrested or charged with a crime than those who did. This claim is supported by the given information: 54% of those who had no preschool education were arrested or charged with a crime, as opposed to only 28% who had preschool education.