How many rolls to see your first six

Question

You roll a fair six-sided die over and over until a six appears, then you stop. On average, how many rolls does it take to get your first six?

Accepted Answer

Each roll is an independent try that succeeds (shows a six) with probability 	frac16. The number of tries until the first success follows what is called a geometric distribution, and its average is just one over the success probability. The intuition is clean: if a six happens on one roll in six on average, then across many rolls you get roughly one six every six rolls, so a fresh wait for a six averages 6 rolls. E[	ext{rolls until first six}] = \frac{1}{1/6} = 6. A quick way to see the "one over p" rule without formulas: let E be the answer. Your first roll always happens. With probability…

How many rolls to see your first six

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