Question

Does crime pay? The FBI Standard Survey of Crimes showed that for about 80% of all property crimes (burglary, larceny, car theft, etc.), the criminals are never found and the case is never solved.† Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetuated by the same criminals. The police are investigating nine property crime cases in this district.

Answer 1

The appropriate answer is "11 crimes".

Explanation:

Let,

The number of crimes be "n".

Now,

⇒
`P(solved \ at \ least \ one) = 1-P(solved \ none \ of \ n)`

or,

⇒
`1-(0.8)^n>0.9`

⇒
`(0.8)^n<0.1`

By taking log both sides, we get

⇒
`n>=(log(0.1))/(log(0.8))`

By putting the values, we get

⇒
`n>=10.31`

`n=11 \ crimes`