JEE 2023 — Mathematics PYQ

Let $\Omega =\{1,2,3,4,5,6\}$ i.e., they are outcome of throwing a dice.

Let $A=$ Getting a number $7$

Now, $P(A)=\frac{\text{Favourable cases}}{\text{Total cases}}=\frac{0}{6}=0$

But $A=\varphi$

$\Rightarrow S_1$ is true.

$B=$ Getting a number < 7

$P(B)=\frac{\text{Favourable cases}}{\text{Total cases}}$

$\Rightarrow P(B)=\frac{6}{6}=1$

Since, $B=\Omega$

$\Rightarrow S_2$ is true.