Vague pronouns are found in sentences where it's not clear which noun the pronoun is referring to. In the sentences provided, the first, second, and fourth sentences contain vague pronouns making it unclear if 'she' refers to Maria or Josie, if 'it' refers to the player's action or to the ball, and if 'she' refers to Lydia or Olivia.
The sentences that have vague pronouns are the ones where it isn't clear to which noun the pronoun is referring. A pronoun should clearly refer to a specific noun, but a vague pronoun makes it unclear. Looking at the provided sentences:
- Maria worked with Josie to complete the project until she had to go home. - It is not clear whether 'she' refers to Maria or Josie.
- The player is running with the ball and it is exciting. - 'It' could refer to the fact that the player is running with the ball or to the ball itself, making 'it' a vague pronoun.
- Lydia met up with Olivia at the library after she finished her research. - 'She' could refer to either Lydia or Olivia.
The other two sentences are clear in their pronoun references, so they do not contain vague pronouns.