medium Probability
A release-checked medium problem for training Dice, Conditional Probability.
Can one create two identical loaded 6-sided dice with the values $1-6$ such that when one throws both dice, each sum from $2$ to $7$ (inclusive on both) appears with equal positive probability? If so, report the probability of rolling the value $1$. If not, report $-1$. Note that other sums besides $2-7$ can appear with positive probability.
This Probability problem is tagged Dice, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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