Regular Expression with odd number of 1's and at least one 0

Question

I am designing a regular expression with an odd number of 1's and at least one 0. Set of strings over {0,1}

So far I have this:

0+1(0+10+1)*0+

Is this correct?

Answer 1

The deterministic finite automaton (DFA) would be

while following the steps described here, I came up with

00*1(11)*0*+1(11)*00*