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Two dice are thrown, What is the probability that the sum of the two faces of the dice is less than 6, if we know that said sum is a multiple of 4?

These kinds of exercises are not my forte, but I'm pretty sure my answer is correct. The solution given is $\frac{3}{10}$, but I think the real solution is $\frac39$, I realized this is conditional probability, so I did $$\frac{\frac{3}{36}}{\frac{9}{36}}$$ Which gave me my answer. Are there any errors? Thanks.

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I agree with you. There are $3$ ways to get $4$, $5$ ways to get $8$ and $1$ way to get $12$

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Your answer is correct. However, if you exchange the conditional statements like this.

What is the probability that the said sum is a multiple of 4 given that sum of the two faces of the dice is less than 6?

Then the answer would be 3/10. (which is the given solution according to you)

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  • $\begingroup$ Thanks, I didn't think about that, the statement has no ambiguity, so I guess either someone messed up either in the statement, or the solutions. $\endgroup$ – Nick Cassol Sep 11 '17 at 20:25

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