Data compiled by the Department of Justice on the number of people arrested for serious crimes (murder, forcible rape, robbery, and so on) 87% were male and 10% were female. Of the males, 26% were under 18, whereas 23% of the females arrested were under 18. If a person arrested for a serious crime was known to be under 18, what is the probability (rounded to two decimal places) that the person is female?
A) 0.26
B) 0.74
C) 0.91
D) 0.09
E) 0.23

Question

Data compiled by the Department of Justice on the number of people arrested for serious crimes (murder, forcible rape, robbery, and so on)  87% were male and 10% were female. Of the males, 26% were under 18, whereas 23% of the females arrested were under 18. If a person arrested for a serious crime  was known to be under 18, what is the probability (rounded to two decimal places) that the person is female?
A) 0.26 
B) 0.74 
C) 0.91 
D) 0.09 
E) 0.23

Quizplus · Accepted Answer

From the given data, we can calculate that the percentage of male arrestees under 18 is 0.87 x 0.26 = 0.2262 and the percentage of female arrestees under 18 is 0.1 x 0.23 = 0.023. We are asked to find the probability that a person arrested for a serious crime under 18 is female, which is the proportion of female arrestees under 18 out of all arrestees under 18, so we can calculate:

(0.023) / (0.2262 + 0.023) = 0.09

Therefore, the probability that the person is female is 0.09, which corresponds to answer choice D.

Data Compiled by the Department of Justice on the Number