Hello,

I have a probability space $\displaystyle (X,\mathcal{A},\mu)$. Considering sets $\displaystyle A$, $\displaystyle B$ and $\displaystyle C$ in $\displaystyle \mathcal{A}$ with:

$\displaystyle \mu(A \cap C) = \mu(A\cap C) = \mu(B\cap C)=\frac{2}{3}$.

How do I begin to show that $\displaystyle \frac{1}{2}\leq\mu(A \cap B \cap C) \leq \frac{2}{3}$?

Appreciate the help!