I am working on a project which is loaded with probability outcomes. To parody a segment of my problem, consider throwing 3 dice (each numbered 1 through 6 as usual). The probability of scoring 3 sixes with one throw (termed a success) = (1/6)^3 or 1/216. If this exercise is repeated n times, there is a greater chance to score a success but there is yet a chance of not scoring (a success) at all, regardless of the value of n. It would sound intuitive that when n=216, at least one success should be registered but this is most certainly not the case as the law of averages fail here.

Now, can someone compute, using bimomial expansion or otherwise, the statistical probability of at least scoring one set of 3 simultanoeus sixes throwing all 3 dice at any one time? What value of n (or limit thereof) attaches to this outcome?

Any help will be appreciated

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