We are tasked with finding the probability that the sum of the two dice rolls, $i + j$, equals 8. The possible outcomes from rolling two fair six-sided dice are pairs $(i, j)$, where $i$ and $j$ are numbers from 1 to 6. Let's break it down step by step:

Total Possible Outcomes

Since each die has 6 sides, there are a total of $6 \times 6 = 36$ possible outcomes when rolling two dice.

Favorable Outcomes

We need to count how many pairs $(i, j)$ satisfy the equation $i + j = 8$. The possible pairs that sum to 8 are:

$(2,6), (3,5), (4,4), (5,3), (6,2)$

These are the five pairs where the sum is exactly 8.

Probability Calculation

The probability of an event is the ratio of favorable outcomes to the total number of possible outcomes. Thus, the probability is:

$P(i + j = 8) = \frac{5}{36}$

Now, dividing and rounding to four decimal places:

$P(i + j = 8) = \frac{5}{36} \approx 0.1389$

Final Answer

The probability that $i + j = 8$ is $\boxed{0.1389}$.

Would you like further details or have any other questions?

Here are 5 related questions for deeper understanding:

1. What is the probability that $i + j = 7$ in the same scenario?
2. How many outcomes result in a sum less than 6?
3. What is the probability that both dice show the same number?
4. If the dice were not fair, how would the probability calculation change?
5. How does the number of favorable outcomes change for different sums?

Tip: When working with probability problems, always start by calculating the total number of possible outcomes.