What is the language recognized by the following deterministic finite-state automaton?

Question

Is the answer:

{w : w ∈ {0*,1*} and w contains at least 3 zero}

correct?

Answer 1

Yes, I think you meant the correct thing, but you should write

$$\{w \in \{0,1\}^* \space | \space w \text{ contains at least 3 0's}\}.$$

As a regular expression, this can be expressed as (as adjan has already done)

$$1^*01^*01^*0(0|1)^*$$