Determining the probability of throwing $8$ with two dice

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Suppose we have two dice. Now we are imposing a condition that the two dice are independent of each other and when we throw, we must have $8$ (that means $6+2 , 5+3$ or $4+4$ etc). Therefore we are throwing two dice at the same time.

What is the probability that we get 8 in each time?

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If first dice gives $r,1\le r\le 6;$ the second needs to give $8-r$

So, $1\le 8-r\le 6\implies 7\ge r\ge 2$

So, $2\le r\le 6$

So, the required probability $\sum_{2\le r\le 6}P(r)P(8-r)=5\cdot\left(\frac16\right)^2$