A 6-faced fair dice is rolled repeatedly till 1 appears for the first time. The probability that the dice is rolled for even number of time is________.

Dear Shiva,

Pr = (6P(r-1) * (r-1)) / 6^r
where the 6P(r-1) is the permutation function.
This gives
P1 = 0
P2 = 1/6
P3 = 10/36 = 5/18
P4 = 60/216 = 5/18
P5 = 5 / 27
P6 = 25/324
P7 = 5/324
P8 = 0
P9 = 0
P10 = 0

b) 1
The sum is the same as saying "What is the probability that the first time you have a repeated number is on the first ten rolls?" Well, we can only roll six times without getting a repeat, in which case the 7th roll would be our last. Therefore we ALWAYS have to get a repeated number in the first ten rolls, so the probability is 1.

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