I need some help in solving the following problem. We roll a fair die repeatedly until see the number $6$. Let $X$ be a random variable is a number of times we roll the die. Let $A$ be the event "The results of all rolls are even numbers". What is the value of $\mathbb{E}(X|A)$?
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See if this helps you: https://www.quora.com/What-is-the-expected-number-of-rolls-of-a-fair-six-sided-die-to-get-a-6-given-that-all-rolls-leading-up-to-that-6-are-even-numbered – Dec 07 '17 at 13:19
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This problem is discussed at https://math.stackexchange.com/questions/2463768/understanding-the-math-behind-elchanan-mossel-s-dice-paradox – Especially Lime Dec 07 '17 at 13:27
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thanks guys. I got it – Valentin Tatarenko Dec 07 '17 at 13:29