Question 1172383
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If their sum is even, it means that EITHER both numbers are odd OR both numbers are even.


Among the numbers 1 to 9 inclusive, there are 5 odd and 4 even numbers.


So,  P(the sum is even) = P(both are odd) + P(both are even) = {{{(5/9)*(4/8) + (4/9)*(3/8)}}} = {{{20/72 + 12/72}}} = {{{32/72}}}.    


From the other hand side,  P(both are odd) = {{{(5/9)*(4/8)}}} = {{{20/72}}}.


Therefore, the conditional probability that both numbers are odd, given that their sum is even, is equal to


    P(final) = {{{P(both_are_odd)/P(the_sum_is_even)}}} = {{{((20/72))/((32/72))}}} = {{{20/32}}} = {{{5/8}}}.    <U>ANSWER</U>
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Solved.