If P AC - P BC and P AC- - P BC- then the relationship between PA and PB is

The correct option is A P ( A )> P ( B ) P(AC)=P(A∩ C)P(C) Now 0 lt;P(C) lt;1 Also, P(BC)=P(B∩ C)P(C) Now P(AC) gt;P(BC) P ...

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Conditional Probability

If P AC > P...

Question

If $P (\frac{A}{C}) > P (\frac{B}{C})$ and $P (\frac{A}{¯ C}) > P (\frac{B}{¯ C})$ then the relationship between $P (A)$ and $P (B)$ is

P (A) = P (B)

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P (A) \leq P (B)

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P (A) > P (B)

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P (A) \geq P (B)

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Solution

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P (B | A) < P (B)

P (A | B)

P (A)

P (B) = \frac{3}{4}, P (A \cap B \cap ¯ C) = \frac{1}{3}

P (¯ A \cap B \cap ¯ C) = \frac{1}{3}

P (B \cap C)

P (A \cup B) = P (A \cap B) \Leftrightarrow

P (A)

P (B)

P (A) = P (B)

(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) .

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