Data compiled by the Department of Justice on the number of

Data compiled by the Department of Justice on the number of people arrested for serious crimes (murder, forcible rape, robbery, and so on) in 1988 revealed that 89% were male and 11% were female. Of the males 30% were under 18, whereas 27% of the females arrested were under 18, what is the probability that the person is female?

Solution

The prob that the person is female is simply : 11% ---> given in the question itself

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However, i believe the question could have been like this :
\"If a person arrested for a serious crime in 1988 was known to be under 18, what is the probability that the person is female?\"

If so, this is how we do it :

ANSWER :

Prob of Males under 18 = 30% of 89% = 26.7% of the total
Probability of Males not under 18 = 70% of 89% = 62.3% of the total
Prob of Females under 18 = 27% of 11% = 2.97% of the total
Prob of females over 18 = 8.03% of the total

Now, we know the person was under 18...

So, P(female under 18) = (2.97) / (2.97 + 26.7)

= 0.100101112234580384226491405460060667340748230535895

10.01% ----> ANSWER