Baran is trying to decide between investing $$10000$ into a savings accounts at a $10\%.$ yearly interest rate or a new stock. The return on the new stock is linked in part to the overall stock market behavior as exhibited by the DOW JONES NDEX. If the DOW JONES INDEX increases on the average during the year then there is a probability of that the stock value will increase. If the DOW JONES INDEX decrases on the average during the year, then there is a probability $0\mathrm{.}3$ that the stock will increase. The probability that the DOW JONES INDEX increases on the average during the coming ycar is $0\mathrm{.}55.$ The set payoff in one year on the investment of $$10,000$ for these events is as follows

$\backslash$table$[[,$STOCK VALUE$],[$Increase$,$Decrease$],[$DOW JONES INDEX Increases,$$8,000,-$$$5,000$