Game show uncertainty in the final round of a tv game

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17.2 Game Show UncertaintyIn the final round of a TV game show, contestants have a chance to increase their current winnings of $1million to $2million. If they are wrong, their prize is decreased to $500,000. A 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?:
19.3 Bicycle Insurance and Information AsymmetryYou sell bicycle theft insurance. If bicycle owners do not know whether they are high- or low-risk consumers, is there an adverse selection problem? There is definitely an adverse selection problem! The consumer :

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