If E and F are events with P(E) le P(F) and P | vedclass

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(D) Given $P(E) \le P(F)$ and $P(E \cap F) > 0.$$P(E) \le P(F)$ implies that the probability of event $E$ is less than or equal to the probability of

Vedclass · Accepted Answer

None of the above implications holds

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(D) Given $P(E) \le P(F)$ and $P(E \cap F) > 0.$$P(E) \le P(F)$ implies that the probability of event $E$ is less than or equal to the probability of event $F$,but it does not imply that $E$ is a subset of $F$ $(E \subseteq F)$.$P(E \cap F) > 0$ implies that the intersection of $E$ and $F$ is not an empty set,meaning there is at least one outcome common to both events.Since $E$ is not necessarily a subset of $F$,the occurrence of $E$ does not guarantee the occurrence of $F$. Similarly,$F$ is not necessarily a subset of $E$,so the occurrence of $F$ does not guarantee the occurrence of $E$.Furthermore,the non-occurrence of $E$ $(\overline{E})$ does not imply the non-occurrence of $F$ $(\overline{F})$.Therefore,none of the given implications necessarily holds.

If $E$ and $F$ are events with $P(E) \le P(F)$ and $P(E \cap F) > 0,$ then

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