If P(A / B) = frac{3}{10}, P(B / A) = frac{4} | vedclass

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(B) Given $P(A / B) = \frac{P(A \cap B)}{P(B)} = \frac{3}{10} \implies P(A \cap B) = \frac{3}{10} P(B)$.$P(B / A) = \frac{P(A \cap B)}{P(A)} = \frac{4

Vedclass · Accepted Answer

$\frac{40}{43}$

Vedclass · Answer

(B) Given $P(A / B) = \frac{P(A \cap B)}{P(B)} = \frac{3}{10} \implies P(A \cap B) = \frac{3}{10} P(B)$.$P(B / A) = \frac{P(A \cap B)}{P(A)} = \frac{4}{5} \implies P(A) = \frac{5}{4} P(A \cap B) = \frac{5}{4} 	imes \frac{3}{10} P(B) = \frac{3}{8} P(B)$.We know $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Given $P(A \cup B) = K P(B)$, so $K P(B) = P(A) + P(B) - P(A \cap B)$.Dividing by $P(B)$, we get $K = \frac{P(A)}{P(B)} + 1 - \frac{P(A \cap B)}{P(B)}$.Substituting the values: $K = \frac{3}{8} + 1 - \frac{3}{10}$.$K = \frac{15 + 40 - 12}{40} = \frac{43}{40}$.Therefore, $\frac{1}{K} = \frac{40}{43}$.

If $P(A / B) = \frac{3}{10}$, $P(B / A) = \frac{4}{5}$ and $P(A \cup B) = K P(B)$, then $\frac{1}{K} =$

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