Two dice are rolled and someone indicates that the two numbers that come up are different. Find the probability that the sum of the two numbers is $8$.
$(2,6)$, $(3,5)$, $(5,3)$, $(6,2)$.
Above are the sums that give $8$. I did not include $(4,4)$ since the question indicated that the number on die must be different from each other. I assume the probability would be $\frac{4}{36}$ since each probability is $\frac{1}{36}$. But my online exercise does not accept this answer. What am I missing?
Best Answer
If you know that both numbers are different, then you have less cases than 36. Actually, you have to eliminate the possibilities $(1,1), (2,2), ..., (6,6)$. So the answer will be $\frac4{30}=\frac2{15}$.