We have four dice in the shape of a tetrahedron. Each dice has faces numbered 2, 0, 1, and 7. If we roll all four dice simultaneously, what is the probability that we can compose the number 2017 using one of the three visible numbers from each dice?
Here is what I tried:
$\frac{3}{4}$x$\frac{3}{4}$x$\frac{3}{4}$x$\frac{3}{4}$=$\frac{81}{256}$
The real answer is $\frac{63}{64}$.
Please help me with this answer!
Best Answer
Out of the visible parts of the dice, 3 parts are visible, the worst case is that all four dice show same visible part, otherwise, $2017$ can be composed.
So let's say there are four numbers the first dice not showing, the remaining three must not be showing the same number, just as the first dice do, which its probability is $[ \frac{1}{4} ]^3$, so the answer is $1-[ \frac{1}{4} ]^3 = \frac{63}{64}$