(C) In probability theory,for a sample space $\Omega$ and an event $A \subseteq \Omega$:$1$. If $P(A) = 0$,it implies that the event $A$ is an impossi

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both $(S1)$ and $(S2)$ are true

(C) In probability theory,for a sample space $\Omega$ and an event $A \subseteq \Omega$:$1$. If $P(A) = 0$,it implies that the event $A$ is an impossible event,which means $A = \phi$. Thus,$(S1)$ is true.$2$. If $P(A) = 1$,it implies that the event $A$ is a sure event,which means $A = \Omega$. Thus,$(S2)$ is true.Therefore,both statements $(S1)$ and $(S2)$ are true.

Class 11 Mathematics Probability Set Based probability

Difficult

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements:
$(S1) : \text{If } P(A) = 0, \text{ then } A = \phi$
$(S2) : \text{If } P(A) = 1, \text{ then } A = \Omega$
Then:

JEE MAIN 2023 All JEE MAIN

A
only $(S1)$ is true
B
only $(S2)$ is true
C
both $(S1)$ and $(S2)$ are true
D
both $(S1)$ and $(S2)$ are false

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Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements:$(S1) : \text{If } P(A) = 0, \text{ then } A = \phi$$(S2) : \text{If } P(A) = 1, \text{ then } A = \Omega$Then:

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If from each of the three boxes containing $3$ white and $1$ black,$2$ white and $2$ black,and $1$ white and $3$ black balls,one ball is drawn at random,then the probability that $2$ white and $1$ black ball will be drawn is

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Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements:
$(S1) : \text{If } P(A) = 0, \text{ then } A = \phi$
$(S2) : \text{If } P(A) = 1, \text{ then } A = \Omega$
Then: