If A and B are two events such that P(A) = fr | vedclass

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(d) We have $P(A \cup B) \ge \max .$ $\{ P(A),\,P(B) \} = \frac{2}{3}$

$P(A \cap B) \le \min .$$\{ P(A),P(B)\} = \frac{1}{2}$

and $P(A \cap B) =

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(d) We have $P(A \cup B) \ge \max .$ $\{ P(A),\,P(B) \} = \frac{2}{3}$

$P(A \cap B) \le \min .$$\{ P(A),P(B)\} = \frac{1}{2}$

and $P(A \cap B) = P(A) + P(B) - P(A \cup B) \ge P(A) - P(B) - 1 = \frac{1}{6}$

$ \Rightarrow \frac{1}{6} \le P(A \cap B) \le \frac{1}{2}$

$P\,(A' \cap B) = P(B) - P(A \cap B)$

Hence $\frac{2}{3} - \frac{1}{2} \le P(A' \cap B) \le \frac{2}{3} - \frac{1}{6}$

$ \Rightarrow \frac{1}{6} \le P(A' \cap B) \le \frac{1}{2}$.

If $A$ and $B$ are two events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{2}{3},$ then

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