The game of Dungeons and Dragons uses nonstandard dice. Consider a die with eight sides marked 1, 2, 3, 4, 5, 6, 7, and 8. (In this problem, "an eight" refers to rolling an eight on either or both dice, while "a total of eight" refers to the sum on the two dice.) List the sample space for yourself in order to answer the following question. What is the probability of rolling exactly one seven with two such dice?
A) $\frac { 7 } { 64 }$
B) $\frac { 5 } { 64 }$
C) $\frac { 7 } { 32 }$
D) $\frac{1}{8}$

E) $\frac { 3 } { 64 }$

Question

The game of Dungeons and Dragons uses nonstandard dice. Consider a die with eight sides marked 1, 2, 3, 4, 5, 6, 7, and 8. (In this problem, "an eight" refers to rolling an eight on either or both dice, while "a total of eight" refers to the sum on the two dice.) List the sample space for yourself in order to answer the following question. What is the probability of rolling exactly one seven with two such dice?
A) $\frac { 7 } { 64 }$
B) $\frac { 5 } { 64 }$
C) $\frac { 7 } { 32 }$
D) $\frac{1}{8}$

E) $\frac { 3 } { 64 }$

Quizplus · Accepted Answer

The sample space is: {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (1,8), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (2,7), (2,8), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (3,7), (3,8), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (4,7), (4,8), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (5,7), (5,8), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6), (6,7), (6,8), (7,2), (7,3), (7,4), (7,5), (7,6), (7,7), (7,8), (8,1), (8,2), (8,3), (8,4), (8,5), (8,6), (8,7), (8,8)}.
We can see that there are seven ways to roll exactly one seven: (1,7), (2,7), (3,7), (4,7), (5,7), (6,7), (7,1), (7,2), (7,3), (7,4), (7,5), (7,6), (7,8). Therefore, the probability is $\frac{7}{64} + \frac{6}{64} = \boxed{	extbf{(C) } \frac{7}{32}}$.

The Game of Dungeons and Dragons Uses Nonstandard Dice 764\frac { 7 } { 64 }647​

The Game of Dungeons and Dragons Uses Nonstandard Dice $\frac { 7 } { 64 }$