Explanation:
a probability is always the ratio of
desired cases / totally possible cases
the "group" is the totally possible cases = 119.
we pick 1 student.
female AND off-campus.
there are only 20 students that satisfy that criteria.
the probabilty for this event is then
20/119 = 0.168067227... ≈ 0.168
male AND on-campus.
there are 34 students that satisfy that criteria.
the probability for this event is then
34/119 = 0.285714286... ≈ 0.286
off-campus OR male.
there are 20+11 = 31 students off-campus.
and there are 34+11 = 45 male students.
the overlapping number of 11 students we need to count only once.
so, there are 20+11+34 = 65 students off-campus or male (incl. the on-campus males, as this is an or-criteria).
the probabilty for this event is then
65/119 = 0.546218487... ≈ 0.546
on-campus OR female.
there are 54+34 = 88 students on-campus.
and there are 54+20 = 74 female students.
the overlapping number of 54 students we need to count only once.
so, there are 54+34+20 = 108 students on-campus or female.
the probabilty for this event is then
108/119 = 0.907563025... ≈ 0.908