There are several parts to this problem, which must be clearly stated for genuine understanding. At a first-principles level, we need to know how many ways the 2 mutual funds can be selected from the 2 categories, as well as how many ways to select at least 1 underperforming fund.
Let's first deal with how many ways we can select 2 funds from the 6 American funds and 2 funds from the 4 international funds. These selections are independent combinations, taken together. So this is calculated as (6C2) • (4C2), which equals 15 • 6, or 90 total ways these can be selected. This will be the denominator of the probability fraction.
Now let's deal with the numerator, which is the number of possible successes. I've found that, whenever the language of "at least one" is used, it's usually easier to find how many ways that the opposite happens and subtract from the total number of possible outcomes.
In this case, the way this doesn't happen is both mutual funds from both categories do not include an underperforming fund.
In the first category, (U.S.), 5 funds do not underperform, and we want to know how many ways we can pick 2 of those funds. This is 5C2, or 10. We can do the same with the international. This would be 3C2, or 3. The total number of ways this happens is 3 • 10, or 30.
Now, don't forget that 30 is how many ways we get a failure, according to out problem. So we get a "success" 90 - 30 ways, or 60.
Finally, we can get our fraction of 60/90, or 2/3.
