Dice Probability ?
When rolling 5 dice, what is the probability of rolling at least one 6, one 5, and one 4.
Is there a Formula Such as P=(1/6)x(1/6)x(1/6)+(1/6)x(1/6). I know the probability
of rolling one of each with 3 dice is 1/216. I don't know how to compute the
additional probability of the other two dice. I am looking for the most basic way to do the math.
The simplest thing I can think of is using inclusion-exclusion.
Originally Posted by Delbert
Let A = event of rolling at least one 6, one 5, and one 4.
Let C = event that a 6 is not rolled.
Let D = event that a 5 is not rolled.
Let E = event that a 4 is not rolled.
Then by inclusion-exclusion,
Then you take
P(C) = P(D) = P(E) = ? (think about it)
P(C ∩ D) = P(C ∩ E) = P(D ∩ E) = ? (think about it)
P(C ∩ D ∩ E) = ?
See how far you can get.