Two six-sided dice are rolled at the same time. The probability that the product of the numbers that both dice land on, is an even number, is x/36. What is the value of x?

To find the probability that the product of the numbers on both dice is an even number, we need to consider the possible outcomes.

Step 1: Determine the total number of outcomes when rolling two six-sided dice. Each die has six possible outcomes, so the total number of outcomes is 6 * 6 = 36.

Step 2: Determine the number of outcomes where the product is an even number. An even number can be obtained by multiplying two even numbers or by multiplying an even number with zero.

• Multiplying two even numbers: There are three even numbers on a six-sided die (2, 4, and 6). So, the number of outcomes where both dice land on even numbers is 3 * 3 = 9.
• Multiplying an even number with zero: There is only one zero on a six-sided die. So, the number of outcomes where one die lands on zero and the other die lands on an even number is 1 * 3 = 3.

Step 3: Add the number of outcomes from step 2 to get the total number of outcomes where the product is an even number: 9 + 3 = 12.

Step 4: Calculate the probability by dividing the number of favorable outcomes (12) by the total number of outcomes (36): 12/36 = 1/3.

Therefore, the value of x is 1.