Let be the set of all students in the <u>c</u>lassroom.
Let and be the sets of students that pass <u>p</u>hysics and <u>m</u>ath, respectively.
We're given
i. We can split up into subsets of students that pass both physics and math and those that pass only physics . These sets are disjoint, so
ii. 9 students fails both subjects, so we find
By the inclusion/exclusion principle,
Using the result from part (i), we have
and so the probability of selecting a student from this set is