3295263856329

482 Mastering Technical Mathematics
Figure 30-4
Venn diagram
showing a pair
of non-disjoint
outcomes.
Figure 30-4 shows this as a Venn diagram. The intersection of probabilities is subtracted
to ensure that the elements common to both sets (represented by the white region where
the two sets overlap) are counted only once.
Imagine that a certain high school has 1000 students. The new swimming and diving
coach, during his first day on the job, is looking for team prospects. Suppose that the
following are true:
• 200 students can swim well enough to make the swimming team.
• 100 students can dive well enough to make the diving team.
• 30 students can make either team or both teams.
If the coach wanders through the school’s hallways blindfolded and picks a student
at random, let’s determine the probabilities, expressed as ratios, that the coach will
pick
• A fast swimmer; call this p(S)
• A good diver; call this p(D)
• Someone good at both swimming and diving; call this p(S D)
• Someone good at either swimming or diving, or both; call this p(S D)
This problem is a little tricky. You can assume that the coach has objective criteria for
evaluating prospective candidates for his teams! That said, you must note that the outcomes
are not mutually exclusive, nor are they independent. There is overlap, and there
is interaction. You can find the first three answers immediately, because you are told the
numbers:
p(S) 200/1000 0.200
p(D) 100/1000 0.100
p(S D) 30/1000 0.030