# Mean Waiting Time

What is the mean waiting time to get two successive throws of 6? What about three, four? And what is the easiest answer to these questions?

>showlarge intrandom(1,1000,6)
[2,  6,  2,  6,  6,  4,  3,  5,  5,  6,  4,  1,  6,  6,  4,  6,  6,  4,
2,  6,  3,  1,  2,  6,  2,  4,  2,  1,  4,  6,  6,  2,  1,  2,  4,  2,
5,  5,  2,  4,  4,  1,  5,  2,  1,  6,  5,  2,  5,  3,  5,  1,  6,  2,
6,  3,  6,  4,  3,  2,  6,  4,  3,  5,  1,  6,  2,  4,  4,  3,  1,  5,
3,  2,  1,  1,  6,  3,  1,  4,  3,  2,  2,  3,  3,  3,  4,  3,  6,  5,
2,  5,  3,  3,  1,  1,  6,  6,  1,  3,  3,  6,  5,  6,  1,  1,  1,  5,
6,  4,  3,  3,  1,  5,  2,  6,  5,  2,  3,  4,  4,  2,  2,  1,  6,  6,
1,  2,  6,  2,  2,  2,  4,  4,  5,  5,  1,  4,  2,  4,  4,  6,  6,  4,
5,  5,  5,  4,  1,  1,  1,  6,  6,  3,  2,  3,  2,  2,  3,  2,  3,  6,
6,  4,  6,  4,  6,  6,  3,  2,  1,  5,  2,  3,  1,  3,  6,  3,  4,  6,
2,  6,  2,  2,  1,  5,  4,  2,  5,  1,  4,  4,  2,  4,  6,  6,  3,  5,
1,  3,  6,  3,  1,  5,  5,  1,  5,  5,  2,  5,  4,  4,  4,  5,  1,  3,
6,  3,  6,  5,  5,  2,  2,  5,  6,  4,  5,  4,  5,  6,  5,  6,  5,  3,
6,  4,  6,  2,  1,  1,  4,  5,  4,  6,  1,  2,  5,  1,  2,  3,  4,  2,
1,  2,  6,  3,  2,  1,  2,  6,  1,  3,  5,  2,  2,  2,  3,  2,  6,  3,
1,  1,  5,  2,  1,  1,  1,  3,  2,  6,  5,  2,  4,  3,  3,  2,  1,  4,
4,  2,  5,  3,  5,  2,  5,  3,  3,  1,  5,  2,  4,  2,  5,  4,  4,  2,
5,  6,  5,  2,  1,  4,  4,  2,  5,  5,  6,  1,  1,  2,  4,  4,  4,  5,
1,  4,  4,  2,  6,  1,  3,  4,  6,  5,  5,  2,  4,  5,  4,  4,  5,  2,
6,  4,  3,  6,  6,  3,  4,  2,  5,  4,  4,  4,  6,  6,  6,  5,  2,  5,
1,  3,  2,  2,  2,  1,  2,  5,  1,  2,  2,  5,  5,  4,  1,  4,  6,  3,
2,  3,  1,  1,  1,  2,  5,  3,  6,  6,  2,  2,  6,  3,  4,  1,  6,  6,
2,  2,  5,  1,  3,  6,  3,  5,  1,  2,  1,  5,  1,  4,  4,  4,  2,  6,
3,  6,  4,  3,  5,  3,  4,  1,  2,  2,  3,  2,  5,  1,  2,  5,  6,  5,
4,  1,  3,  2,  6,  6,  5,  3,  5,  5,  4,  3,  1,  2,  5,  6,  4,  3,
5,  5,  4,  5,  5,  2,  3,  3,  3,  1,  6,  4,  4,  2,  6,  3,  5,  3,
2,  1,  5,  3,  6,  1,  2,  1,  6,  2,  3,  1,  1,  1,  2,  6,  2,  1,
5,  2,  5,  4,  6,  5,  6,  2,  1,  6,  6,  4,  2,  5,  6,  1,  2,  1,
5,  3,  3,  1,  3,  4,  1,  5,  6,  1,  4,  5,  5,  2,  2,  2,  4,  5,
4,  4,  6,  3,  6,  1,  4,  5,  3,  3,  1,  6,  5,  4,  6,  5,  5,  2,
4,  3,  4,  2,  6,  4,  4,  6,  5,  6,  2,  5,  5,  6,  5,  3,  4,  2,
3,  4,  2,  3,  3,  1,  1,  4,  2,  5,  4,  5,  2,  3,  1,  5,  1,  1,
2,  3,  4,  6,  3,  5,  4,  2,  1,  2,  5,  1,  6,  4,  2,  1,  6,  3,
6,  2,  6,  4,  4,  4,  5,  6,  6,  6,  5,  2,  1,  4,  4,  1,  5,  2,
2,  3,  3,  3,  6,  6,  5,  1,  4,  3,  4,  4,  3,  6,  6,  2,  2,  6,
2,  2,  5,  2,  5,  2,  3,  4,  4,  3,  4,  6,  6,  1,  3,  4,  2,  5,
3,  2,  2,  3,  2,  6,  3,  2,  5,  6,  1,  1,  2,  5,  4,  6,  4,  6,
4,  3,  2,  1,  5,  3,  6,  2,  2,  6,  4,  5,  3,  4,  1,  6,  2,  6,
2,  2,  6,  6,  3,  6,  1,  1,  6,  1,  4,  3,  5,  4,  1,  3,  5,  6,
1,  1,  2,  5,  2,  3,  2,  5,  4,  1,  4,  5,  5,  3,  3,  2,  4,  2,
4,  5,  6,  5,  1,  3,  5,  5,  5,  4,  1,  6,  1,  4,  4,  1,  3,  3,
2,  6,  3,  5,  3,  4,  2,  2,  6,  3,  1,  4,  5,  3,  3,  5,  5,  1,
3,  6,  1,  1,  6,  4,  1,  1,  3,  3,  4,  1,  2,  3,  6,  4,  2,  3,
3,  6,  6,  3,  3,  6,  6,  2,  3,  5,  6,  5,  3,  5,  2,  5,  2,  6,
5,  6,  2,  1,  3,  1,  3,  4,  2,  3,  2,  5,  1,  3,  3,  5,  4,  2,
3,  6,  3,  6,  6,  3,  6,  5,  3,  4,  6,  5,  5,  6,  6,  1,  5,  3,
2,  4,  3,  5,  1,  1,  3,  2,  2,  3,  1,  2,  3,  2,  4,  1,  3,  3,
4,  4,  4,  3,  4,  2,  2,  5,  3,  3,  5,  5,  5,  2,  6,  4,  3,  2,
3,  4,  5,  4,  4,  4,  2,  3,  1,  3,  3,  6,  4,  6,  4,  2,  5,  2,
3,  1,  6,  6,  6,  1,  6,  6,  3,  5,  2,  1,  5,  2,  4,  2,  2,  6,
3,  6,  2,  6,  6,  2,  6,  6,  3,  3,  2,  2,  4,  6,  6,  5,  6,  3,
1,  3,  2,  4,  5,  1,  6,  2,  2,  5,  2,  4,  6,  1,  4,  4,  5,  6,
1,  5,  5,  1,  4,  1,  5,  4,  6,  4,  1,  5,  1,  2,  4,  5,  5,  3,
6,  1,  4,  3,  3,  5,  1,  4,  2,  5,  3,  4,  6,  5,  5,  5,  6,  5,
1,  5,  2,  4,  4,  4,  3,  6,  3,  3,  4,  3,  3,  2,  6,  1,  3,  6,
6,  6,  1,  2,  4,  5,  2,  5,  3,  2]


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