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Default Probability Question


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

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Myle
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