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a city is made up of two types of people the x's and the y's. the x's constitute 15% of the population and the y's constitute the rest. x’s are twice as likely to commit crimes than y’s. that is 4% of x’s commit crimes while 2% of y’s commit crimes. a crime has been committed downtown and you are trying to narrow down the suspects what are the chances that an x committed this crime

Answer :

Answer:

Step-by-step explanation:

We know that:

[tex]x=.15z\\y=.85z\\[/tex]

Since 4% of the x's commit crimes, we can substitute:

[tex].04x=.04(.15z)=.006z[/tex]

Therefore the chances of x committing the crime are .6%

Answer:

57.5%

Step-by-step explanation:

We know that the total number of the population is made up of 15% x's and 85% of y's and let the total amount of population be z:

[tex]z=0.15\cdot{x}+0.85\cdot{y}[/tex]

we also know that x's are twice as likely to commit crimes than y's:

[tex]x=2\cdot{y}[/tex]

Therefore is we can solve for x by substituting y=x/2 into the first equation:

[tex]z=0.15\cdot{x}+0.85\cdot{x/2}[/tex]

[tex]z=0.575\cdot{x}[/tex]

Therefore the chances of the x's committing the crime is 57.5% of the x's are likely to commit the crime.

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