Exercises

Fun Class Activities:

1. A card is drawn from a standard deck. What is the probability that it's a $2$, given that it's black?
2. If $P(A \cap B) = 0.15$, and $P(B) = 0.3$, compute $P(A | B)$.
3. If $P(A) = 0.4$, $P(B) = 0.5$, and $P(A \cap B) = 0.2$, are $A$ and $B$ independent?
4. If two events are mutually exclusive, what is $P(A \cap B)$? Why?
5. If $P(A)=0.2$, $P(B|A)=0.6$, $P(B|A^c)=0.3$, and $P(A^c)=0.8$, find $P(A|B)$.