Hi all, I'm new to the forum
I have a bit of a problem in working out how to calculate some probabilities involving multiple dice rolls for a wargame. All the websites I have consulted so far assume I want o roll all my dice and add them up, but that's not the case.
Essentially this is an OR operator rather than an AND operator. Assuming fair six-sided dice, numbered 1 to 6, I understand that if I roll one die, the chances of rolling a '6' is 1/5; the chances of rolling a 5 or higher (so 5 or 6) is 2/6 = 1/3 and so on. And that the chances of rolling 5 or greater and then another 5 or greater with the next roll is 1/3 x 1/3 or 1 \ 9
But what I'm trying to do here is to work out a formula so that if I roll a series of, say, four dice, what are the chances of rolling a 5 or 6 with any one of those rolls? Or, to put it another way, if I roll four dice at the same time, what are the chances of at least one of them having a 5 or a 6 showing?
Clearly it is not as simple as just adding 1/3 plus 1/3 plus 1/3 plus 1/3 because then the probability would be over 100%, which is of course incorrect. I could roll four '1's, for example. So it's and OR operator: Die 1 can roll a 5 or 6, OR die 2 can roll a 5 or 6, and so on up to die 4.
So what does this look like iin terms of formulae, please, and how is that formula derived?
Thanks in advance
I have a bit of a problem in working out how to calculate some probabilities involving multiple dice rolls for a wargame. All the websites I have consulted so far assume I want o roll all my dice and add them up, but that's not the case.
Essentially this is an OR operator rather than an AND operator. Assuming fair six-sided dice, numbered 1 to 6, I understand that if I roll one die, the chances of rolling a '6' is 1/5; the chances of rolling a 5 or higher (so 5 or 6) is 2/6 = 1/3 and so on. And that the chances of rolling 5 or greater and then another 5 or greater with the next roll is 1/3 x 1/3 or 1 \ 9
But what I'm trying to do here is to work out a formula so that if I roll a series of, say, four dice, what are the chances of rolling a 5 or 6 with any one of those rolls? Or, to put it another way, if I roll four dice at the same time, what are the chances of at least one of them having a 5 or a 6 showing?
Clearly it is not as simple as just adding 1/3 plus 1/3 plus 1/3 plus 1/3 because then the probability would be over 100%, which is of course incorrect. I could roll four '1's, for example. So it's and OR operator: Die 1 can roll a 5 or 6, OR die 2 can roll a 5 or 6, and so on up to die 4.
So what does this look like iin terms of formulae, please, and how is that formula derived?
Thanks in advance