A man was arrested on suspicion of murder. Let us denote the event \'the man is

Question

A man was arrested on suspicion of murder. Let us denote the event 'the man is guilty' by G. The investigating officer collected all the relevant information, added his impressions of the suspect and arrived at the conclusion that the man's probability of guilt was 0.60. As the investigation went on, it was learned (beyond any reasonable doubt) that the murderer's blood type was O. The relative frequency of blood type O in the population is 0.33 (that is the probability that a randomly selected person in the population has blood type O). The suspect's blood was tested and found to be O. Compute the probability of this suspect's guilt considering this new data. Suppose both the murderer's and the suspect's blood types were found (with certainty) to be A. The relative frequency of blood type A in the population is 0.42. How would the probability of guilt in that case compare with the same probability I part (a)? Would it be greater, smaller, or equal? Explain.

Explanation / Answer

a. Probability that suspects' guilt

=P(blood group O/suspects' guilt )/P(/suspects' guilt)

=0.33/0.60

=0.55

b. Probability that suspects' guilt

=P(blood group A/suspects' guilt )/P(/suspects' guilt)

=0.42/0.60

=0.70

The probabaility is greater than part-(a)

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