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

To solve this problem, we need to understand that an even product can only be obtained if at least one of the factors is even. In the case of a dice, the even numbers are 2, 4, and 6.

Step 1: Determine the total number of outcomes When three dice are rolled, the total number of outcomes is 666 = 216. This is because each die has 6 faces and we have 3 dice.

Step 2: Determine the favorable outcomes The only way to get an odd product with three dice is if all the numbers rolled are odd. The odd numbers on a die are 1, 3, and 5. So, the number of ways to get an odd product is 333 = 27. This is because we have 3 odd numbers on a die and we have 3 dice.

Step 3: Determine the number of outcomes where the product is even Since the only way to get an odd product is if all numbers are odd, all other outcomes will result in an even product. So, the number of outcomes where the product is even is the total number of outcomes minus the number of outcomes where the product is odd. This is 216 - 27 = 189.

Step 4: Calculate the probability The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So, the probability that the product of the numbers rolled on three dice is even is 189/216 = 0.875 or 87.5%.