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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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