Final answer:
The probability of rolling two 4's on two six-sided dice is 1/36, which is approximately 0.0278 when expressed as a decimal rounded to four decimal places.
Step-by-step explanation:
The probability of rolling two six-sided dice and obtaining two 4's can be calculated using the sample space of the two dice. Since each die is independent and has six sides, the total number of outcomes when rolling two dice is 6 × 6, which equals 36. Now, there is only one outcome that will result in two 4's, namely (4,4). Therefore, the probability of rolling two 4's is the number of favorable outcomes (which is 1) divided by the total number of outcomes (which is 36).
So, using probability notation, the probability (P) of rolling two 4's (event A) is P(A) = 1/36. To express it as a decimal rounded to four decimal places, it would be approximately 0.0278.
Keep in mind that probability is the measure of how likely an event is to occur. The more times you roll the dice, the closer you would expect your experimental results to get to this theoretical probability, due to the law of large numbers.