W contains at least two 0s and at most one 1

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Construct a deterministic finite-state automaton that recognizes the set of all bit strings that contain an even number of 0 $\mathrm{s}$ and an odd number of 1 $\mathrm{s}$ .

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we have the alphabet {0,1}.

{w|w contains at least two 0s and at most one 1}

It tried this: (However I'm not sure if it's correct. If it's incorrect why?)