Minimal DFA contains 4 states only. the following figure shows minimal DFA for a given regular expression:

$L={\epsilon,ba,baba,bababa….,aba,aaba,aaaba,….ababa, aababa...\infty}$

only four state is sufficient

Dknights Given DFA accepts $\epsilon$ because initial state in the final state

4 State

abhinowKatore above finite automata is not DFA, not even minimal.