A survey of needy and disabled youths showed that 50% of those who had no presch

Question

A survey of needy and disabled youths showed that 50% of those who had no preschool education were arrested or charged with a crime by the time they were 19, whereas only 25% 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 25% of them had attended preschool. (a) What percentage of the youths arrested or charged with a crime had no preschool education? % (b) What would this figure be if 75% of the youths had attended preschool? %

Explanation / Answer

Answer:

S: Preschool, NS: No preschool

A: Arrested or charged

a).

P(S) =0.25    P( NS)=0.75

P( A/S)=0.25   P( A/NS) =0.50

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

=0.25*0.25+0.75*0.50

=0.4375

or

=44%

b).

P(S) =0.75    P( NS)=0.25

P( A/S)=0.25   P( A/NS) =0.50

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

=0.75*0.25+0.25*0.50

=0.3125

Or

=31%

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