The sentence "Alma and her brother Jose has won the state robotics competition for high school students" must be corrected. The correct answer is "have won".
The sentence provided must be corrected because there must be subject/verb agreement. In other words, the subject and the verb must agree in number. As the subject of the sentence provided is a compound subject, that is, a subject composed of two nouns ("Alma" and "(her) brother"), it must be followed by a plural verb. Therefore, the subject must be followed by "have" instead of "has", which is a singular verb. Moreover, the sentence is referring to an event that actually happened in the past; therefore, the third and fourth options are also incorrect.