Question 1194049
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One standard die is rolled twice. Find the probability of getting on two rolls of the die a pair whose sum is even.
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<pre>
The sum is even if and only if


        (a)  both outcomes are even

    or

        (b)  both outcomes are odd.


In case (a), the probability of this event is, OBVIOUSLY,  {{{(1/2)*(1/2)}}} = {{{1/4}}}.


In case (b), the probability of this event is, OBVIOUSLY, the same {{{(1/2)*(1/2)}}} = {{{1/4}}}.


The events (a) and (b) are mutually excluded;  THEREFORE,  the final <U>ANSWER</U>  to the problem's question is  {{{1/4}}} + {{{1/4}}} = {{{1/2}}}.
</pre>

Solved and thoroughly explained.