A six-sided die (with numbers 1 through 6) and an eight-sided die (with numbers 1 through 8) are rolled. what is the probability that there is exactly one 6 showing? express your answer as a common fraction

In this case, there are two major possibilities.

First: The six sided die shows 6 and the eight sided die shows any number except 6.

Second: The eight sided die shows 6 and the six sided die shows any number except 6.

The total possibility would be the sum of the first case and the second case.

Calculating for each possibility:

First case: In this case, since we want to show the number 6 on the six sided die, therefore the probability is 1/6. While on the eight sided die, we want any number except 6 therefore the probability is 7/8. Hence, the combined probability is the product:

P (1st case) = (1/6) (7/8) = 7/48

Second case: In this case, since we want to show the number 6 on the eight sided die, therefore the probability is 1/8. While on the six sided die, we want any number except 6 therefore the probability is 5/6. Hence, the combined probability is the product:

P (2nd case) = (1/8) (5/6) = 5/48

The total probability is the sum of 1st and 2nd case:

P (total) = P (1st case) + P (2nd case)

P (total) = 7/48 + 5/48

P (total) = 12/48 = 1/4