Probability 2 Question 3
3. If $E$ and $F$ are events with $P(E) \leq P(F)$ and $P(E \cap F)>0$, then which one is not correct? (1998, 2M)
(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
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Answer:
Correct Answer: 3. (a)
Solution:
- It is given that, $P(E) \leq P(F) \Rightarrow E \subseteq F$
and $\quad P(E \cap F)>0 \Rightarrow E \subset F$
(a) occurrence of $E \Rightarrow$ occurrence of $F$
[from Eq. (i)]
(b) occurrence of $F \Rightarrow$ occurrence of $E$
(c) non-occurrence of $E \Rightarrow$ occurrence of $F$
[from Eq. (ii)]
Hence, option (c) is not correct.
[from Eq. (i)]
