Some ex-cons spend the rest of their lives either free, on trial, in jail, or on probation. At the start of each year statistics show that there is 50% chance that a free ex-con will commit a new crime and go on trial. The judge may send the ex-con to jail with the probability .6 or grant probation with a probability of A. Once in jail, 10% of commit new crimes and are arraigned for new trials, 50% will go back to finish their sentence for violating probation orders, and 10% will be set free for lack of evidence. Taxpayers underwrite the cost associated with the punishment of the ex-felons. It is estimated that a trial will cost about $5000, an average jail sentence will cost $20,000 and an average probation will cost $2000.
a. Determine the expected cost per ex-con.
b. How often does an ex-con return to jail? Go on trial? Be set free.