1
$\begingroup$

Problem Statement: You roll a fair six-sided die until all six numbers have been rolled at least once. What is the expected value of that ?

Can you write different ways to solve this problem ?

$\endgroup$
0
$\begingroup$

Without loss of generality let us focus on one of the numbers, say $1$. The probability that we see $1$ on the $n^{\text{th}}$ attempt given that we did not observe $1$ on the previous $n-1$ tries is given by:

${(\frac{5}{6})}^{n-1} \cdot \frac{1}{6}$

You can use the above to compute the expected value of the number of attempts to make to see $1$. We then multiply the above by $6$ to get the answer we seek.

$\endgroup$
  • $\begingroup$ Can you please solve it and find the solution for completeness ? $\endgroup$ – Abhisek Oct 8 '17 at 17:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.