Big Envelope · Quanteaser

You have two envelopes in front of you with $â¬X$ and $â¬2X$ , where $X \sim \unif{0}{a}$ for some $a > 0$ that is known. You select one of them uniformly at random and look at the value inside. After looking inside, you have the option to keep the envelope you have or switch. Under optimal strategy, what is the probability we obtain the envelope with $â¬2X$ when $a = 100$ ?

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