Final answer:
To find the probability that the absolute value of the difference of two fair, six-sided dice is 3, divide the number of favorable outcomes by the total number of possible outcomes.
Step-by-step explanation:
To find the probability that the absolute value of the difference of two fair, six-sided dice is 3, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.Let's consider the value on the first die as x and the value on the second die as y. The absolute value of the difference between x and y can be 3 in the following cases: (x=1, y=4) or (x=4, y=1) or (x=2, y=5) or (x=5, y=2) or (x=3, y=6) or (x=6, y=3). So there are 6 favorable outcomes.Since there are 6 possible outcomes for each die (1, 2, 3, 4, 5, 6), there are a total of 6 * 6 = 36 possible outcomes.Therefore, the probability is 6 / 36 = 1 / 6.