.
In a high school graduating class of 100 students, 54 studied mathematics, 69 studied history,
and 35 studied both mathematics and history. If one of these students is selected at random,
find the probability that:
(a) the student took mathematics or history;
(b) the student did not take either of these subjects;
(c) the student took history but not mathematics.
~~~~~~~~~~~~~~~~~~
(a) P(M or H) = P(M) + P(H) - P(M and H) = = = = 0.88.
(b) P(neither M nor H) = 1 - P(M or H) = 1 - = = 0.12. This probability is the COMPLEMENT to (a).
(c) P(H not M) = P(H \ (M and H)) = P(H) - P(M and H) = - = = = 0.34.
Solved.
----------------
To see many other similar (and different) solved problems, look into the lessons
- Elementary operations on sets help solving Probability problems
- Elementary operations on sets help solving Probability problems - REVISITED
in this site.