( d ) Pistudent will graduate and student is male ) ( e ) Pistudent will graduate ) Note that those who will graduate are either males who will graduate or females who will graduate ( f 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 plwill graduate female ) different ? The term given refers to the sample space of all students , while the term and refers to restricting the sample space to females only ! ' This is by chance . These probabilities are typically the same . These probabilities are the same . ! " The term and refers to the sample space of all students , while the term given refers to restricting the sample space to females only