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 10% of the population. The footprint is a size 13 men's shoe and only 7% 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

Question

Paul Bender

Mathematics

16 February, 11:01

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 10% of the population. The footprint is a size 13 men's shoe and only 7% 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

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Grayson · Answer 1

There is a 0.175% chance of finding such a person who has all three characteristics.

Out of 4,000 people, 7 people would likely to match all three characteristics.

Step-by-step explanation:

A crime has been committed and after analyzing the evidence, police has found out that:

The criminal's blood type is a type found in only 10% of the population. The criminal's footprint is a size 13 men's shoe and only 7% of the population wears such shoe size. Only 25% of the population owns clothing made from a fabric that matches the thread samples found at the scene.

We required to find out the probability of selecting a random person who would match all of these characteristics.

Since it is given that the three characteristics are independent of each other then the required probability is

P (all 3 characteristics) = P (1st characteristic) * P (2nd characteristic) * P (3rd characteristic)

P (all 3 characteristics) = (10/100) * (7/100) * (25/100)

P (all 3 characteristics) = 1750/1,000,000

P (all 3 characteristics) = 7/4000

P (all 3 characteristics) = 0.00175

P (all 3 characteristics) = 0.175%

So out of 4,000 people, 7 people would likely to match all three characteristics.

or

There is a 0.175% chance of finding such a person who has all three characteristics