# Some ex-cons spend the rest of their lives in one of four states

August 31, 2017

Question
Some ex-cons spend the rest of their lives in one of four 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 or 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?

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