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At the scene of a crime, the police have found a blood stain, a footprint, and s

ID: 3122006 • Letter: A

Question

At the scene of a crime, the police have found a blood stain, a footprint, and some threads from a fabric. All are presumed to have been left by the person who committed the crime. After analyzing the evidence it is found that: The blood type is a type found in only 30% of the population. The footprint is a size 13 men's shoe and only 6% of the population wears that shoe size. Only 25% of the population owns clothing made from a fabric that matches the thread samples found at the scene. The police have a suspect who matches all of the criteria. He has the same blood type, the same shoe size, and owns clothing matching the threads found at the scene of the crime. While this is only circumstantial evidence, what is the probability that a random person would match all of these characteristics if the three characteristics are assumed to be independent of each other? (Give your answer correct to four decimal places)

Explanation / Answer

Solution:

It is given that

three characteristics are assumed to be independent of each other

therefore they  are all independent events

hence

a suspect who matches the blood type is a type found in only 30% of the population = 30/100

a suspect who matches the footprint is a size 13 men's shoe and are only 6% of the population = 6/100

a suspect who matches the clothing made from the same fabric is 25 % of the population = 25/100

since all are independent

therefore

the probability that a random person would match all of these characteristics = (30/100) * ( 6/100) * (25/100)

= 4500/1000000

= 45/10000

45 out of 10000 random person would match all of these characteristics

Answer