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Conditional Probability

If A and B ar...

Question

If A and B are two events then

P (A \cap B) \geq P (A) + P (B) - 1

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P (A \cap B) \geq P (A) + P (B)

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P (A \cap B) = P (A) + P (B) - P (A \cup B)

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P (A \cap B) = P (A) . P (B)

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Solution

The correct options are
A $P (A \cap B) \geq P (A) + P (B) - 1$
C $P (A \cap B) = P (A) + P (B) - P (A \cup B)$
$P (A \cup B) = P (A) + P (B) - P (A \cap B)$
$P (A \cup B) \leq 1$
$∴ P (A) + P (B) - P (A \cap B) \leq 1$

Suggest Corrections

Similar questions

A

(A)

(B)

P (A / B) = P (B / A)

P (A) = P (B)

(A \cap B) \neq ϕ

P (A / B) = \frac{P (A \cap B)}{P (B)}

P (B / A) = \frac{P (A \cap B)}{P (A)}

(i) P (A) = \frac{1}{3}, P (B) = \frac{1}{4} and P (A \cup B) = \frac{5}{12}, then find P (A | B) and P (B | A) . (ii) P (A) = \frac{6}{11}, P (B) = \frac{5}{11} and P (A \cup B) = \frac{7}{11}, then find P (A \cap B), P (A | B) and P (B | A) . (iii) P (A) = \frac{7}{13}, P (B) = \frac{9}{13} and P (A \cap B) = \frac{4}{13}, then find P (A | B) . (iv) P (A) = \frac{1}{2}, P (B) = \frac{1}{3} and P (A \cap B) = \frac{1}{4}, then find P (A | B), P (B | A), P (A | B) and P (A | B) .

\frac{6}{11},

\frac{5}{11}

\frac{7}{11},

\frac{7}{13},

\frac{9}{13}

\frac{4}{13},

P (A / B) .

P (A / B) > P (A)

P (B / A) > P (B)

P (A / B) = \frac{P (A \cap B)}{P (B)}

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