Suppose I have one each of d4, d6, d8, d10, d12, and d20 (these are all commonly used dice in games).
It is easy to determine each of their individual probabilities of rolling a 1:
d4: 0.250
d6: 0.167
d8: 0.125
d10: 0.100
d12: 0.083
d20: 0.050
How do I determine the probability of rolling at least 3 ones when rolling all six dice?
I've thought about viewing it as probability of exactly 3 plus probability of exactly 4 etc... Even then, I'm not sure how to approach it when the probabilities aren't the same.
This problem was created as a simplified version of a much larger problem with several hundred distinct probabilities where I need to find the probability of at least half. I'm hoping to find a process that can be converted into something I can run with code.
It is easy to determine each of their individual probabilities of rolling a 1:
d4: 0.250
d6: 0.167
d8: 0.125
d10: 0.100
d12: 0.083
d20: 0.050
How do I determine the probability of rolling at least 3 ones when rolling all six dice?
I've thought about viewing it as probability of exactly 3 plus probability of exactly 4 etc... Even then, I'm not sure how to approach it when the probabilities aren't the same.
This problem was created as a simplified version of a much larger problem with several hundred distinct probabilities where I need to find the probability of at least half. I'm hoping to find a process that can be converted into something I can run with code.