I am working on the following problem.
If you toss two dice, what is the probability that the first dice shows a face of 6, given that the sum of both faces is an 8?
Am I wrong to assume that both rolls are independent? If not, wouldn't the probability just be the following:
$$\frac{1}{6} \approx 16.67\%$$
Thank you!
Yes, you are wrong, because the information that the sum is $8$ means the rolls are not independent. In particular, the first roll cannot be $1$ (nor can the second).