Type of Attack Given that an assault victim is selected, what is the likelihood that the criminal is a stranger?
A) 757/2000
B) 1787/2000
C) 757/1426
D) 1426/2000

Question

Type of Attack  Given that an assault victim is selected, what is the likelihood that the criminal is a stranger?
A) 757/2000 
B) 1787/2000 
C) 757/1426 
D) 1426/2000

Quizplus · Accepted Answer

The probability of the criminal being a stranger can be calculated using Bayes' theorem. Let A be the event that the victim is selected and B be the event that the criminal is a stranger. We want to find P(B|A).

P(A) = 1 since we are given that an assault victim is selected.
P(B) = 757/2000 since there are 757 out of 2000 attacks where the criminal is a stranger.
P(A|B) = 1 since if the criminal is a stranger, then they must have assaulted a stranger.
P(B|A) = P(A|B)P(B) / P(A)
         = (1 * 757/2000) / 1
         = 757/2000

Therefore, the likelihood that the criminal is a stranger given that an assault victim is selected is 757/2000, which is choice C.

Type of Attack Given That an Assault Victim Is