5.3 Exercise 1 — Applied Probability

Suppose $\left\{A , B\right\} ci \left|\right. C$ and $\left\{A , B\right\} ci \left|\right. C^{c}$ , $P \left(C\right) = 0 . 7$ , and

P \left(\right. A \left|\right. C \left.\right) = 0 . 4 P \left(\right. B \left|\right. C \left.\right) = 0 . 6 P \left(\right. A \left|\right. C^{c} \left.\right) = 0 . 3 P \left(\right. B \left|\right. C^{c} \left.\right) = 0 . 2

Show whether or not the pair $\left\{A , B\right\}$ is independent.

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