Pronouns rename nouns. The pronouns must agree with the nouns they rename in gender and quantity. This sentence would be incorrect, though common:
- The environment in which a person lives determines their believe systems.
In this case, “their” would be incorrect, as it is a plural pronoun renaming the singular noun “person.” This is a common error due to the current vogue of political correctness (not a bad thing) which shows the deficiencies in our language, since we cannot call human beings by the neutral pronoun “it.” Therefore, to correct this mistake, substitute “her or his” for “their”:
- The environment in which a person lives determines her or his believe systems.
Or change the initial noun to a plural:
- The environment in which persons live determines their believe systems.
The latter example avoids that tricky flaw in the language a bit more eloquently than the first solution, though either would be correct. Neither seem very satisfying, however; perhaps revising the entire sentence might be in order:
- Environment determines a person’s beliefs.