Obtain your best roll!

The possibility to get at least 1 six in 6 rolls of a six-sided die is \(A\).

The possibility to get at least 2 sixes in 12 rolls of the same six-sided die is \(B\).

The possibility to get at least 3 sixes in 18 rolls of the same six-sided die is \(C\)

\[ D = 6A + 12B + 18C \]

Find the value of \(D\), correct to one decimal place.

Details and Assumptions

  • Assume they are all unbiased six-sided die.

  • Each event is independent from one another.

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