You Play A Game Where You First Choose A Positive Integernand Thenflip A Fair Coinnt 3305430

You play a game where you first choose a positive integernand thenflip a fair coinntimes. You win a prize if you get exactly 2 heads. How should youchoosento maximize your chance of winning? What is the chance if winning withan optimal choice ofn? There are two equally good choices for the bestn. Findboth.Hint: Letfnbe the probability that you get exactly two heads out ofncoinflips. Derive conditions whenfn< fn+1andfn> fn+1.

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