I can't seem to wrap my head around how to calculate this, nor the reasoning behind it.
Say you have 3 10-sided dice. 2 dice have 8 "winning" faces and 2 "losing" faces. So an 80% chance of winning. The third dice has 5 "winning" and 5 "losing" sides, so a 50% chance of winning.
If you roll all three of these dice at the same time:
-What is the probability of at least 1 dice winning.
-What is the probability of at least 2 dice winning.
-What is the probability of all 3 winning.
From what I've seen I can calculate the probability of all 3 winning by doing:
0.8 x 0.8 x 0.5=0.32
A 32% chance of all 3 winning at the same time.
But what about the others, I can't seem to figure it out.
You're right, I flubbed my calculation. The probability of at least two winning is 87.04%.
For your other question, the key words are at least. The probability of at least one die winning, which includes the probability of more dice also winning (two or three).
I'm on mobile so I can't do it now, but if you're interested you could create a table of every possibility and their respective probabilities. That table should add up to exactly 100%, and you can add up all the valid combinations for a given criteria to verify the shorter math we did before.