Question

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 1

Explanation:

We know that:

`x=.15z\\y=.85z\\`

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

`.04x=.04(.15z)=.006z`

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

Answer 2

57.5%

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:

`z=0.15\cdot{x}+0.85\cdot{y}`

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

`x=2\cdot{y}`

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

`z=0.15\cdot{x}+0.85\cdot{x/2}`

`z=0.575\cdot{x}`

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