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.
(a) What is the overall reporting rate for crimes in the city?
(b) If a crime in progress is reported to the police, what is the probability that the crime is violent? What is the probability that it is nonviolent?
(c) Refer to part b. If a crime in progress is reported to the police, why is it more likely that it is a nonviolent crime? Wouldn't violent crimes be more likely to be reported? Can you explain these results?