82% of the bullets recovered at crime scenes are damaged (D) [Pr(D)]. Of the rec

Question

82% of the bullets recovered at crime scenes are damaged (D) [Pr(D)]. Of the recovered undamaged bullets (D'), 85% are undamaged enough to undergo comparative examination (C) [Pr(C|D')], whereas 40% of damaged bullets (D) are not able to undergo comparative examination (C) [Pr(C'|D)]. Suppose a bullet is recovered from a crime scene. Compute the following probabilities: The probability that the bullet is not damaged Pr(D')?: If the bullet is not damaged, the probability that it can undergo comparative examination Pr(C|D)?: If the bullet is not damaged, the probability that it cannot undergo comparative examination Pr(C'|D')?: The probability that the bullet is damaged and can undergo comparative examination Pr(DnC)?:

Explanation / Answer

PROBABILITY THAT BULLET IS DAMAGED = 0.82

A) THEREFORE THE PROBABILITY THAT BULLET IS NOT DAMAGED = 1 - 0.82 = 0.18

B) IT IS GIVEN THAT 40% OF DAMAGED BULLET ARE NOT UNDER GONE EXAMINLATION

THEREFORE THE UNDAMAGED BULLET WILL UNDERGO EXAMINATION = 1-0.40 = 0.6

C) IT IS GIVEN THAT 85% OF THE NON DAMAGED WILL UNDERGO EXAMINATION

THEREFORE THE PROBABILITY THAT THE NON DAMAGED WILL NOT UNDERGO EXAMINATION = 1-0.85 = 0.15

D)PROBABILITY THAT THE BULLET IS DAMAGED AND WILL UNDERGO EXAMINATION = 0.6*0.82 = 0.492

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