Solutions - 5020-02

(1) State the inclusion-exclusion principle:

$$P[A\cup B]=P[A]+P[B]-P[A\cap B]$$

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(2) Derive a contradiction:

Given $P[A]=0.5$ and $P[B]=0.7$, we have $P[A]+P[B]=1.2$.

Since $P[A\cup B]\le 1$, it follows that $P[A\cap B]\ge 0.2$.

Therefore $P[A\cap B]=0.001$ is impossible.