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

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14.Probability

medium

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

A

Occurrence of $E \Rightarrow $ Occurrence of $F$

B

Occurrence of $F \Rightarrow $Occurrence of $E$

C

Non-occurrence of $E \Rightarrow $ Non-occurrence of $F$

D

None of the above implications holds

(IIT-1998)

Solution

(d) $P(E) \le P(F) \Rightarrow n(E) \le n(F)$

$P(E \cap F) > 0 \Rightarrow E \cap F \ne \phi $

These do not mean that $E$ is a sub-set of $F$ or $F$ is a sub-set of $E.$

$i.e.,$ $E \subseteq F$ or $F \subseteq E$ or $\overline E \subseteq \overline F$.

Standard 11

Mathematics

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