What is the probability of rolling 4 dice and getting at least one 4 and at least one 2? Dice are 6 sided.
2026-03-27 05:37:42.1774589862
Probability of rolling 4 dice
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Hint/Setup:
This is an example of a question where it is far easier to calculate the probability of the complementary event, in other words the probability that this doesn't happen.
If we didn't successfully get at least one $4$ and at least one $2$, then that means in the four throws of the dice, we didn't get any $4$'s or we didn't get any $2$'s, possibly both.
From here, you should probably use inclusion-exclusion over the events "didn't roll any $4$'s" and "didn't roll any $2$'s." Remember that inclusion exclusion implies $Pr(A\cup B)=Pr(A)+Pr(B)-Pr(A\cap B)$
Finally, once we know the probability of not rolling any $4$'s or not rolling any $2$'s, to find the original probability we were interested in, subtract this away from $1$.