I keep on throwing a fair die repeatedly till the cumulative sum reaches or crosses 100. What is the probability that the last throw was a six? This needs to be solved without asymptotic assumptions. Thanks a lot!
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You might get some useful ideas from the closely related thread at https://stats.stackexchange.com/questions/145621. – whuber Jul 27 '17 at 23:39
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Whuber, thanks for your suggestion. So, it seems we cannot find a closed-form solution without assuming 100 to be a large number, right? That was where I got stuck, and posted this in the first place. – Preetam Pal Jul 28 '17 at 20:59
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That thread shows just the opposite: it explains how you can compute the value exactly and shows why it will be very close to $2/7$. Indeed, the answer is a rational number which, in reduced form, is a quotient of two 71-digit numbers and is about 4e-15 less than $2/7$. – whuber Jul 28 '17 at 22:22