Does crime pay? The FBI Standard Survey of Crimes shows 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 perpetrated by the same criminals. The police are investigating six property-crime cases in this district.
(a) What is the probability that none of the crimes will ever be solved?
(b) What is the probability that at least one crime will be solved?
(c) What is the expected number of crimes that will be solved? What is the standard deviation?