Probability?

Question

City crime records show that 20% of all crimes are violent, and 80% are nonviolent,
involving theft, forgery, and so on. Ninety percent of violent crimes are reported versus 70%
of nonviolent crimes. If a crime in progress is reported to the police, what is the probability
that the crime is violent?

Answer 1

ironduke, you got the first step of the answer.

The total of all crimes is divided up among reported violent crime, unreported violent crime, reported non-violent crime and unreported non-violent crime.

Reported violent crime = 20% * 90% = 18% of all crime
Unreported violent crime = 20% * 10% = 2% of all crime
Reported non-violent crime = 80% * 70% = 56% of all crime
Unreported non-violent crime = 80% * 30% = 24% of all crime

Of all crimes, only 74% are reported (18% + 56%). Of these 74%, 18% are violent, so therefore dividing 18 by 74, you get 24.32%. Your answer to a if a crime is reported to the police, 24.32% of the time it will be a violent crime.

Answer 2

.2 * .9 = .18 = 18%