Final answer:
Any of the three individuals can be committed against their will to a psychiatric hospital if their condition poses a danger to themselves or others, they are unable to care for themselves, or they lack the capacity to make decisions about their own treatment.
Step-by-step explanation:
In this case, any of the three individuals can be committed against their will to a psychiatric hospital.
Carole, who has schizophrenia and refuses to take her medications, can be committed if her condition poses a danger to herself or others, and if she lacks insight into her illness.
Tina, who is homeless and has schizophrenia, can be committed if she is unable to care for herself, poses a danger to herself or others, or is unable to provide informed consent for treatment.
Kathie, who has schizophrenia and has been threatening to hurt people, can be committed if she poses a danger to herself or others.
In general, individuals with severe mental illnesses like schizophrenia can be involuntarily committed if their condition poses a danger to themselves or others, if they are unable to care for themselves, or if they lack the capacity to make decisions about their own treatment.