The events described the phrases "will graduate and is female" and "will graduate, given female" seem to be describing the same students. why are the probabilities p(will graduate and is female) and p(will graduate | female) different? i) the term given refers to the sample space of all students, while the term and refers to restricting the sample space to females only. ii) this is by chance. these probabilities are typically the same. ii) these probabilities are the same. iv) the term and refers to the sample space of all students, while the term given refers to restricting the sample space to females only.