In the game “Now or Then” on the television show The Price is Right, the contestant faces a wheel with 6 sectors. Each sector contains a grocery item and a price, and the contestant must decide whether the price is “now” (i.e., the item’s price the day of the taping) or “then” (the price at some specified past date, such as September 2003). The contestant wins a prize (bedroom furniture, a Caribbean cruise, etc.) if he/she guesses correctly on three adjacent sectors. That is, numbering the sectors 1–6 clockwise, correct guesses on sectors 5, 6, and 1 wins the prize but not on sectors 5, 6, and 3, since the latter are not all adjacent. (The contestant gets to guess on all six sectors, if need be.) Write a simulation program to estimate the probability the contestant wins the prize, assuming her/his guesses are independent from item to item. Provide estimated probabilities under of the following assumptions: 

(1) Each guess is “wild” and thus has probability .5 of being correct, and .

(2) The contestant is a good shopper, with probability .8 of being correct on any item.