Five identical dices are rolled together, what is the probability that the product of all three outcomes on the three dices will be even?

\(\frac{31}{32}\)

*Product of all three digits will be even if at least one of the digits is even. So we can calculate and eliminate the no of chances when all the digits are odd and all other combinations will have at least one even number to make the product even.

⇒ P (product will be even) = 1 – P (product will be odd)

⇒ Probability to get odd on one dice =\(\frac{3}{6}\) = \(\frac{1}{2}\)

⇒ Probability of getting odd number on all five dices= \(\frac{1}{2}\) × \(\frac{1}{2}\) × \(\frac{1}{2}\) × \(\frac{1}{2}\) × \(\frac{1}{2}\)

⇒ Probability (product will be odd) =\(\frac{1}{32}\)

So, Probability (product will be even) = 1 – \(\frac{1}{32}\)  = \(\frac{31}{32}\)

Hence, option C is correct.