Let's see what a typed tree diagram looks like....
O 3 odds makes an ODD sum; probability (5/9)(4/8)(3/7) = 60/504
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O - E 2 odds 1 even makes an EVEN sum; probability (5/9)(4/8)(4/7) = 80/504
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O - E - O 2 odds 1 even makes an EVEN sum; probability (5/9)(4/8)(4/7) = 80/504
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E 1 odd 2 evens makes an ODD sum; probability (5/9)(4/8)(3/7) = 60/504
E 3 evens makes an EVEN sum; probability (4/9)(3/8)(2/7) = 24/504
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E - O 2 evens 1 odd makes an ODD sum; probability (4/9)(3/8)(5/7) = 60/504
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E - O - E 2 evens 1 odd makes an ODD sum; probability (4/9)(5/8)(3/7) = 60/504
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O 1 even 2 odds makes an EVEN sum; probability (4/9)(5/8)(4/7) = 80/504
The probability of an odd sum is (60+60+60+60)/504 = 240/504 = 10/21
The probability of an even sum is (80+80+24+80)/504 = 264/504 = 11/21
Tree diagrams are useful in solving relatively simple probability problems; and they are a good aid in visualizing how the answer is obtained. But they become extremely awkward very quickly as the problem get more complicated.
A much faster path to the answer is using basic combinatorics.
To get an odd sum when drawing 3 of the 9 marbles, you have to choose either 3 of the 5 odd and 0 of the 4 even, or 1 of the 5 odd and 2 of the 4 even. The probability of doing that is
To get an even sum when drawing 3 of the 9 marbles, you have to choose either 0 of the 5 odd and 3 of the 4 even, or 2 of the 5 odd and 1 of the 4 even. The probability of doing that is