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 9% of the population wears that shoe size. • Only 30% 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.)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 9% of the population wears that shoe size.
Only 30% 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.)
Transcribed Image Text: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 9% of the population wears that shoe size. Only 30% 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.)
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