Someone double check my math, please.

I'm converting a board game from using D10 to multiple D6 and I want to make sure I'm calculating the probabilities right.

So if a 'hit' occurs on a 5 or 6, the odds of a single hit is obviously 1/3.

So for two dice, the odds of a single hit is: P = 1 - (2/3)^2 ??

And then the odds of at least one hit on N dice is P = 1 - (2/3)^N ?

Do I just multiply those probabilities to get the odds of, 2 or more hits?

So the odds of M hits on N dices is P^M?

Seems like I'm missing something, but I don't have my textbooks with me and I'm having to rely on web based math sites.

I know I can trust TR. (<--- memescape material).

ETA: Fixed basic prob cuz I can't read my own equations. (I did that part right in my spreadsheet).

I'm converting a board game from using D10 to multiple D6 and I want to make sure I'm calculating the probabilities right.

So if a 'hit' occurs on a 5 or 6, the odds of a single hit is obviously 1/3.

So for two dice, the odds of a single hit is: P = 1 - (2/3)^2 ??

And then the odds of at least one hit on N dice is P = 1 - (2/3)^N ?

Do I just multiply those probabilities to get the odds of, 2 or more hits?

So the odds of M hits on N dices is P^M?

Seems like I'm missing something, but I don't have my textbooks with me and I'm having to rely on web based math sites.

I know I can trust TR. (<--- memescape material).

ETA: Fixed basic prob cuz I can't read my own equations. (I did that part right in my spreadsheet).