Calculating pi using a probabilistic method

In probability theory, each discrete random variable X has a Probability Mass Function (PMF) from which we can extract the probability of every possible outcome of X. In addition, there is a function called mean (or expectation) E[X], which give as the outcome we should expect from the random variable X. We exploit this attribute in order to (approximately) calculate pi.

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The prisoner’s dilemma

Three prisoners know that one of them is going to be executed. Agony overcame one of them (prisoner A) and he begged the guard to tell him who of them is the unlucky. After some thinking, the guard decides to reveal someone, other than him, who’s not gonna perish.

He now regrets for asking, because, previously, he had a 2/3 chance to stay intact but now only 1/2. Is his deduction correct?

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