Public Intoxication charge is usually not considered as a traffic offense in any state.You must answer the question on deferrment as written.Please check with www.ncdd.com for a lawyer near you I do not practice in Texas and this answer is for general information purposes.
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Public intoxication is not a traffic offense. It is a violation of the penal laws of Texas. It means that the person accused / convicted is a danger to themselves or others.
Some times people think it is the same as a traffic offense because it has the same penalty penalty as many traffic offenses - it is punishable by a fine only (except after 2 or 3 offenses it becomes a Class B misdemeanor punishable by up to 6 months in jail and a fine up to $2,000.)
If you received deferred adjudication for public intoxication, the truthful answer would be yes, you have received a probation (and yes, you have a conviction for Class C public intoxication.)
You are probably safe in marking no to being on probation, you weren't it was a deferred. Traffic violations are class c misdemeanors and usually aren't traceble, just like P.I.s.