If PA - 713- PB - 913 and PA- B - 413- find PA- B-

P(A/ B) = P(A∩ B)P(B) = 4/139/13 = 49 . ...

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Conditional Probability

If PA = 713...

Question

If $P (A) = \frac{7}{13}, P (B) = \frac{9}{13}$ and $P (A \cap B) = \frac{4}{13}$ , find $P (A / B)$ .

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Solution

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P (A) = \frac{7}{13}

P (B) = \frac{9}{13}

P (A \cup B) = \frac{12}{13}

P (A) = \frac{7}{13}, P (B) = \frac{9}{13}

P (A \cap B) = \frac{4}{13}

P (A / B)

P (A \cup B)

2 P (A) = P (B) = \frac{5}{13}

P (A | B) = \frac{2}{5}

P (A \cup B) \times 100

(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) .

P (A \cup B) = \frac{5}{6}

P (A \cap B) = \frac{1}{3}, P (B) = \frac{1}{3} . Find P (A) and P (A') .

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