3. Some ex-cons spend the rest of their lives in one fOUT of states: 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 probability .6 Qr grant probation with probability .4. Once in jail, 10% of ex-cons will be set free for good behavior. Of those who are on probation, 10% 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 costs 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 period will cost $2000.

(a) Determine the expected cost per ex-con.

(b) How often does an ex-con return to jail? Go on trial? Get set free?