Bayes’ theorem
\[P(A|B) = \frac{P(A\cap B)}{P(B)} = \frac{P(B|A)P(A)}{P(B)}\]
Contents
1 Failing in math and/or programming
Probability of failing in math: $P(M)=0.3$
Probability of failing in programming: $P(P)=0.2$
Are these two events related or independent?
Probability of failing in both math and programming: $P(M\cap P)=0.1$
What is the probability of failing in either math or programming $P(M\cup P)$?
What is the probability of failing in programming when you learned that you failed in math $P(P|M)$?