Average probablity to get a specific outcome on a ten sided dice
A man is playing a game with a ten-sided die, he will roll it every minute and will win if it gives the number $10$. On average, how many minutes would it take him to win the game?
My working -
Probability the man does not win on the first try = $9/10$
On his second try, it is = $9/10*9/10$
On the third, it is = $(9/10)^3$
to infinity
That means avg number of tries the game lasts = $9/10 + (9/10)^2 + (9/10)^3+\dots$ which converges to $9$.
Therefore on average, it should take him $9$ minutes to win. But my intuition said it should be $10$ tries because there are $10$ possibilities and it should take $10$ minutes to get all the possible outcomes. Can anyone explain why my intuition is wrong?
$\endgroup$ 01 Answer
$\begingroup$It may be because of a trivial mistake, because you forgot that the first roll can be rolled instantly.
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