3.2 Exercise 17

Since $P \left(\right. \cdot \left|\right. B \left.\right)$ is a probability measure for a given B, we must have $P \left(\right. A \left|\right. B \left.\right) + P \left(\right. A^{c} \left|\right. B \left.\right) = 1$. Construct an example to show that in general $P \left(\right. A \left|\right. B \left.\right) + P \left(\right. A \left|\right. B^{c} \left.\right) \neq 1$.