Probability Question

[Myles]

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

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

Any help will be appreciate

 

[Jerry W. Lewis]

Your question is not well posed. If you are asking about throwing n dice
triplets, where each triplet is uniquely identified, then you have already
explained why the number of triple 6's would be Binomial (n,1/216).
Otherwise you need to state more clearly just what you are asking.

Jerry