Question

If you roll a fair six-sided die and a fair four-sided die, what is the probability that the dice add to 7?

Answer 1

1/6.

For any given roll on a four-sided die, there is exactly one roll on a six-sided die (1/6 chance) which will sum to 7.

Since it doesn’t matter what you roll on the four-sided die, the chance is always 1/6 with a fair six-sided die.

One interesting result of this is that only the 6-sided die has the be fair for this result to hold. The 4-sided die can be very biased in any direction and the final result will still be 1/6.