17 2 game show uncertainty in the final round of a tv

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17-2 Game Show Uncertainty In the final round of a TV game show, contestants have a chance to increase their current winnings of $1 million dollars to $2 million dollars. If they are wrong, their prize is decreased to $500,000. The contestant thinks his guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?
This problem can also be examine another way It costs $1 million to play; if you are right, you win $2 million, if you are wrong, you win $500,000. Expected value of playing is $1 million (0.5*2000000 + 0.5*500000)= $1,250,000 which is higher than the cost of playing The minimum probability of a guess to make playing still profitable is 33.3%. $1,000,000(x) + (-$500,000)(1-x) = 0 $1,000,000x -$500,000 + $500,000x = 0 $1,500,000x = $500,000 X = ($500,000/$1,500,000) X = 1/3 = 33.3% 19-3 Bicycle Insurance and Information Asymmetry You sell bicycle theft insurance. If bicycle owners do not know whether they are high- or low-risk consumers, is there an adverse selection problem?
20-3 Locator Beacons for Lost Hikers Lightweight personal locator beacons are now available to hikers that make it easier for the Forest Service’s rescue teams to locate those lost or in trouble in the wilderness. How will this affect the costs that the Forest Service incurs?

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