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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!

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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).

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  • $\begingroup$ I see what you are saying. Thank you for the information! $\endgroup$ – Lee Dec 4 '18 at 3:02

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