Three identical dices are rolled together, what is the probability that the product of all three outcomes on the three dices will be even?Options5/187/81/83/4

To solve this problem, we need to understand that a product will be even if at least one of the factors is even.

Step 1: Identify 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: Identify the favorable outcomes A die has 3 even numbers (2, 4, 6) and 3 odd numbers (1, 3, 5). If we want the product to be even, at least one die must show an even number. The only case when the product is not even is when all three dice show odd numbers. The probability of getting an odd number on a die is 1/2. So, the probability of getting odd numbers on all three dice is (1/2)(1/2)(1/2) = 1/8.

Step 3: Calculate the probability of the product being even The probability of the product being even is 1 - the probability of the product being odd. So, the probability of the product being even is 1 - 1/8 = 7/8.

So, the correct answer is 7/8.