Question: i have this regular expression: ((a|b)*|a*(ba*)) that is supposed to accept all strings of a's and b's that do not contain the subsequence abb. is

i have this regular expression:
((a|b)*|a*(ba*))
that is supposed to accept all strings of a's and b's that do not contain the subsequence abb.
is my regular expression correct?
and how will the drawing of the finite automata for this expression be?
*if there is something wrong please correct it and give me an explanation.

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