Probability of rolling a $6$ with $2$ dice (that both have a second $6$)

Question

Ok, this is a slightly weird question because its not using regular dice. Long story short, these dice have $2$ sides with the same symbol on them, so I need to know the probability of rolling AT LEAST ONE of this side with the $2$ dice. I can find the probability of landing doubles and landing exactly one. But I don't know the chance of at least one with both.

Answer 1

Basically, let the die have the markings on the faces as: $$A, A, B, C, D, E$$ The probability of rolling an $A$ is thus: $P_A=\frac13$ along with $P_B=P_C=P_D=P_E=\frac16$.

Note that $$P_{\text{At least one A}} = 1- P_{\text{No} A_{\text{Die 1}}}P_{\text{No} A_{\text{Die 2}}} $$ $$=1-\left(\frac23\right)^2=\frac59$$