One of the boxes that Joshua and Wendy unpack has Joshua's collection of board games.  Michael, Wendy, Alexis, and Joshua decide to play one of them, a game called $\textit{Risk}$ that involves rolling ordinary six-sided dice to determine the outcomes of strategic battles.  Wendy has never played before, so early on Michael explains a bit of strategy.

"You have the first move and you occupy three of the four territories in the Australian continent.  You'll want to attack Joshua in Indonesia so that you can claim the Australian continent which will give you bonus armies on your next turn."

"Don't tell her $\textit{that!}$" complains Joshua.

Wendy and Joshua begin rolling dice to determine the outcome of their struggle over Indonesia.  Joshua rolls extremely well, overcoming longshot odds to hold off Wendy's attack.  Finally, Wendy is left with one chance.  Wendy and Joshua each roll just one six-sided die.  Wendy wins if her roll is $\textit{higher}$ than Joshua's roll.  Let $a$ and $b$ be relatively prime positive integers so that $a/b$ is the probability that Wendy rolls higher, giving her control over the continent of Australia.  Find the value of $a+b$.
1. To determine the probability that Wendy rolls a higher number than Joshua, we first need to consider all possible outcomes when both roll a six-sided die. Each die has 6 faces, so there are a total of \(6 \times 6 = 36\) possible outcomes.

2. We need to count the number of outcomes where Wendy's roll is higher than Joshua's roll. Let's list these outcomes:
   - If Wendy rolls a 2, Joshua must roll a 1.
   - If Wendy rolls a 3, Joshua can roll a 1 or 2.
   - If Wendy rolls a 4, Joshua can roll a 1, 2, or 3.
   - If Wendy rolls a 5, Joshua can roll a 1, 2, 3, or 4.
   - If Wendy rolls a 6, Joshua can roll a 1, 2, 3, 4, or 5.

3. Counting these outcomes:
   - For Wendy rolling a 2: 1 outcome (Joshua rolls 1)
   - For Wendy rolling a 3: 2 outcomes (Joshua rolls 1 or 2)
   - For Wendy rolling a 4: 3 outcomes (Joshua rolls 1, 2, or 3)
   - For Wendy rolling a 5: 4 outcomes (Joshua rolls 1, 2, 3, or 4)
   - For Wendy rolling a 6: 5 outcomes (Joshua rolls 1, 2, 3, 4, or 5)

4. Summing these outcomes, we get:
   \[
   1 + 2 + 3 + 4 + 5 = 15
   \]

5. Therefore, there are 15 favorable outcomes where Wendy's roll is higher than Joshua's roll out of 36 possible outcomes.

6. The probability that Wendy rolls higher than Joshua is:
   \[
   \frac{15}{36} = \frac{5}{12}
   \]

7. Since \(a\) and \(b\) are relatively prime positive integers such that \(\frac{a}{b} = \frac{5}{12}\), we have \(a = 5\) and \(b = 12\).

8. The value of \(a + b\) is:
   \[
   5 + 12 = 17
   \]

The final answer is \(\boxed{17}\).