In a group of 101 students 40 are juniors, 50 are female,
and 22 are female juniors. Find the
probability that a student picked
this group at random is either a junior or female.
Note that P(junior) = 40/101 and P(female) = 50/101, and
P(junior and female) = 22/101. Thus
P(junior or female) = 40/101 + 50/101
– 22/101 = 68/101
This makes sense since 68 of the 101 students are juniors
Not sure why? When we add 40 juniors to 50 females
and get a total of 90, we have overcounted. The 22 female
juniors were counted twice; 90
minus 22 makes 68 students who are juniors or female.