SOLUTION: 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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Question 1194049: One standard die is rolled twice. Find the probability of getting on two rolls of the die a pair whose sum is even.
Answer by ikleyn(52855) About Me  (Show Source):
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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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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,  %281%2F2%29%2A%281%2F2%29 = 1%2F4.


In case (b), the probability of this event is, OBVIOUSLY, the same %281%2F2%29%2A%281%2F2%29 = 1%2F4.


The events (a) and (b) are mutually excluded;  THEREFORE,  the final ANSWER  to the problem's question is  1%2F4 + 1%2F4 = 1%2F2.

Solved and thoroughly explained.