Question

A survey of needy and disabled youths showed that 48% of those who had no preschool education were arrested or charged with a crime by the time they were 19, whereas only 34% 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 14% 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 86% of the youths had attended preschool?

Answer 1

Answer:

a)

Given,

Let us assume that S be the preschool

NS be the no preschool

And A be the Arrested or charged

P(S) = 0.14

P( NS) = 1 - 0.14

= 0.86

P( A/S) = 0.34

P( A/NS) = 0.48

Let us consider,

P(A) = P(S) * P( A/S) + P(NS) * P( A/NS)

substitute values

= 0.14 * 0.34 + 0.86 * 0.48

= 0.4604

P(A) = 46 %

b).

P(S) = 0.86

P( NS) = 0.14

P( A/S) = 0.34

P( A/NS) = 0.48

let us consider,

P(A) = P(S) * P( A/S) + P(NS) * P( A/NS)

= 0.86 * 0.34 + 0.14 * 0.48

= 0.3596

= 35.96 %

P(A) = 36%