# Probability of the first die

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).