Here's the question:

Let's say die #1 has 6 sides. And die #2 has 6 sides.

I know that both #1 & #2, because they have the same number of sides, each have a 66.7% chance of rolling 3 or better.

Ok, that's simple enough. But here's where the dice mechanic comes in.

What if I say. Roll 2 six-sided dice, and you need to roll 3 or better on at least one of them.

What is the percentage chance of succeeding when I roll both dice, but only need a 3 or better on one of them?

Now... what happens when the dice have different numbers of sides. For example, what if die #1 has six sides, but die #2 has eight sides?

What is the percentage chance of at least one of these dice rolling 3 or better? I know that die #1 (six sides) has a 66.7% chance, and die #2 (eight sides) has a 75% chance, but what percentage of success do we have if they are both rolled, but only one needs to hit 3 or better?

What about 8 sided + 10 sided vs. a target number of 6 or better?

For the life of me I can't figure out the formula. Help!