-=Probability. Will choose BEST answer-=?

Question

Data compiled by the Department of Justice on the number of people arrested in a certain year or serious crimes (murder, rape, robbery, and so on) 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.

A) What is the probability that a person arrested for serious crime in that year was under 18?

B) If a person arrested for a serious crime in that year is known to be under 18, what is the probability that the person is female?
28 minutes ago

Anonymous · Accepted Answer

A.
Probability that an arrested person will be under 18 is
0.89 x 0.30   +   0.11 x 0.27  =  0.2967.
or a 29.67 per cent chance of being u-18.

B
Probability that a male arrested is under 18 is 0.89 x 0.30  = 0.267.
Probability that a female arrested is under 18 is 0.11 x 0.27  =  0.0297.
So inversely, the prob that a person under 18 when arrested is female is 
0.0297/0.2967 = 0.1001
And prob that the person under 18 is male is 0.267/0.2967 = 0.8998
So the answer is:  just over a 10 per cent chance.

Waheed · Answer

A)
Probability of Male under 18 = 0.89 x 0.3 = 26.7%
Probability  of woman under 18 is = 0.11 x 0.27 = 2.97 %
Total 26.7 + 2.97 = 29.67 % ans.

B)  2.97 / 29.67 = 0.100 i.e. 10 % ans.

cidyah · Answer

M=Male arrested
F=Female arrested
P(M)=0.89
P(F)=0.11
U= Under 18
P(U/M) = 0.30
P(U/F) = 0.27

A) P(U) = [P(M) P(U/M)+P(F) P(U/F)] = 0.2967

B)
Applying Bayes' Theorem,
P(F/U)= P(F) P(U/F) /   [P(M) P(U/M)+P(F) P(U/F)]
P(F/U) = (0.11)*(0.27) / 0.2967 = 0.0297/0.2967 
=0.1001

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-=Probability. Will choose BEST answer-=?

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