die is rolled until all 6 faces have show , what is E(x)

[wind]

In an experiment a die is rolled repeatedly until all 6 faces have finally shown, what is the expected waiting time for this event to occur?

E(x)=q/p

but i dont know what p is... would it be 6!/6^6 or 1/6

 

[pka]

Wind, it seems to me that you have a mistaken idea about ‘wait-times and expectation’. This is a rather well know problem in negative binomial distributions. The expected number of tosses is given by
\(\displaystyle \L 6\left( {1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{6}} \right) \approx 14.7\). If you have a good mathematics library see the collector’s problem in PROBABILITY by Jim Pitman.