Multiply 3 Dice

For the outcome to be even is the same as the outcome not being odd. For the outcome to be odd, all three dice need to be odd, respectively:

• 1*1*1 = 1 (odd)
• 3*3*3 = 27 (odd)
• 5*5*5 = 125 (odd)

and also all combinations of the odd numbers result in odd outcomes, like:

• 1*1*3 = 3 (odd)
• 3*3*5 = 45 (odd)
• etc.

Basically, multiplying odd numbers with each other results in an odd outcome. If ANY even number comes in play, then we have "a number" multiplying "an even number", which will always result in an even number. So, "odd * even * odd" will also result in even.

So, in any other scenario than multiplying three odd numbers, the product will be even. Therefore, the probability that the product is even is, given that half of the sides of the dice are odd ({1,3,5} vs {2,4,6}) equal to \begin{equation} P(even \; product) = 1 - P(only \; odd \; product) \end{equation} \begin{equation} P(even \; product) = 1 - (\frac{1}{2})^3 = \frac{7}{8} \end{equation}