In class we have been told (for now) to use Venn diagrams to solve probability questions, we were also set this question for homework. Instead of answers, a tip, or a nudge in the right direction would be help me the most.
Two events $A$ and $B$ are such that $P(A) = \frac{1}{3}$ and $P(B) = \frac{1}{2}$. Calculate $P(A'\cap B)$ when:
i) $P(A \cap B) = \frac{1}{8}$.
ii) $A$ and $B$ are mutually exclusive
iii) $A$ is a subset of $B$
Here's my working for part i)
$P(A'\cap B) = P(B) – P(A\cap B)$
$\therefore P(A'\cap B) = \frac{3}{8}$
Part 2, and three are more elusive, though. I know mutually exclsuive means they can't both happen at the same time. Does this mean it's $\frac{2}{3}$, or $\frac{1}{2}$?
Best Answer
It is the probability of the intersection of $A'$ and $B$, so it cannot be bigger than $P(B)$
In fact for (ii) it is $\frac12$
For (iii): $A \subset B \implies A \cap B = A$