If A and B are two events such that P(A) = 21 and P(B) = 32, then show that (a) P(A∪B)≥32(b)61≤P(A∩B)≤21 (c ) P(A∩B)≤31(d)61≤P(A∩B)≤21

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If A and B are two events such that P(A) = {{{1}}}{{{2}}} and

Question

If A and B are two events such that P(A) = $\frac{1}{2}$ and P(B) = $\frac{2}{3}$ , then show that
(a) $P (A \cup B) \geq \frac{2}{3} (b) \frac{1}{6} \leq P (A \cap B) \leq \frac{1}{2}$
(c ) $P (A \cap \overline{B}) \leq \frac{1}{3} (d) \frac{1}{6} \leq P (\overline{A} \cap B) \leq \frac{1}{2}$

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Elijah Discussed

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

\frac{1}{2}

and P(B) =

\frac{2}{3}

, then show that
(a)

P (A \cup B) \geq \frac{2}{3} (b) \frac{1}{6} \leq P (A \cap B) \leq \frac{1}{2}

(c )

P (A \cap \overline{B}) \leq \frac{1}{3} (d) \frac{1}{6} \leq P (\overline{A} \cap B) \leq \frac{1}{2}

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Question Text

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

\frac{1}{2}

and P(B) =

\frac{2}{3}

, then show that
(a)

P (A \cup B) \geq \frac{2}{3} (b) \frac{1}{6} \leq P (A \cap B) \leq \frac{1}{2}

(c )

P (A \cap \overline{B}) \leq \frac{1}{3} (d) \frac{1}{6} \leq P (\overline{A} \cap B) \leq \frac{1}{2}