<s>[INST] Pair of die and probability A pair of dice is loaded. The probability that a 2 appears on the first
die is 3/13 and the probability that a 4 appears on the second die is
3/13. Other outcomes for each die appear with probability 2/13. What
is the probability of 6 appearing as the sum of the numbers when the
two dice are rolled?
 [/INST] Add up the following:


*

*Probability of $1$ on 1st dice and $5$ on 2nd dice: $\frac{2}{13}\cdot\frac{2}{13}$

*Probability of $2$ on 1st dice and $4$ on 2nd dice: $\frac{3}{13}\cdot\frac{3}{13}$

*Probability of $3$ on 1st dice and $3$ on 2nd dice: $\frac{2}{13}\cdot\frac{2}{13}$

*Probability of $4$ on 1st dice and $2$ on 2nd dice: $\frac{2}{13}\cdot\frac{2}{13}$

*Probability of $5$ on 1st dice and $1$ on 2nd dice: $\frac{2}{13}\cdot\frac{2}{13}$


And you get $\frac{25}{169}$
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