Let A and E be any two events with positive p | vedclass

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(A) Let $A$ and $E$ be any two events with positive probabilities.Consider Statement $- 1$:$P(E/A) = \frac{P(E \cap A)}{P(A)}$. Since $P(A) \leq 1$,we

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Both the statements are true

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(A) Let $A$ and $E$ be any two events with positive probabilities.Consider Statement $- 1$:$P(E/A) = \frac{P(E \cap A)}{P(A)}$. Since $P(A) \leq 1$,we have $\frac{1}{P(A)} \geq 1$. Therefore,$P(E/A) = \frac{P(E \cap A)}{P(A)} \geq P(E \cap A)$.We know that $P(A/E)P(E) = P(A \cap E)$.Since $P(E \cap A) = P(A \cap E)$,it follows that $P(E/A) \geq P(A \cap E) = P(A/E)P(E)$.Thus,Statement $- 1$ is true.Consider Statement $- 2$:$P(A/E) = \frac{P(A \cap E)}{P(E)}$. Since $P(E) \leq 1$,we have $\frac{1}{P(E)} \geq 1$. Therefore,$P(A/E) = \frac{P(A \cap E)}{P(E)} \geq P(A \cap E)$.Thus,Statement $- 2$ is true.

Let $A$ and $E$ be any two events with positive probabilities:
Statement $- 1$: $P(E/A) \geq P(A/E)P(E)$
Statement $- 2$: $P(A/E) \geq P(A \cap E)$

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Let $A$ and $E$ be any two events with positive probabilities:Statement $- 1$: $P(E/A) \geq P(A/E)P(E)$Statement $- 2$: $P(A/E) \geq P(A \cap E)$