If $S$ be the sample space of a random experiment $\xi$ and $P$ be a probability function defined on the power set $P(S)$ of $\mathrm{S}$, then which one of the following is not satisfied by P? (i) $\mathrm{P}(\phi)=0$ (ii) If $\mathrm{E}^{\mathrm{c}}$ is the complementary event of $\mathrm{E}$,…

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If $S$ be the sample space of a random experiment $\xi$ and $P$ be a probability function defined on the power set $P(S)$ of $\mathrm{S}$, then which one of the following is not satisfied by P? (i) $\mathrm{P}(\phi)=0$ (ii) If $\mathrm{E}^{\mathrm{c}}$ is the complementary event of $\mathrm{E}$, then $\mathrm{P}\left(\mathrm{E}^{\mathrm{c}}\right)=$ $1-P(E)$ (iii) $0 \leq \mathrm{P}(\mathrm{E}) \leq 1, \forall \mathrm{E} \subseteq \mathrm{S}$ (iv) If $\mathrm{E}_1 \subseteq \mathrm{E}_2 \mathrm{P}\left(\mathrm{E}_2\right) \leq \mathrm{P}\left(\mathrm{E}_1\right)$

Aicharya · Accepted Answer

If $E_1 \subseteq E_2$ Then $P\left(E_1ight) \leq P\left(E_2ight)$ $	herefore$ Statement (iv) is not satisfied by $P$

If $S$ be the sample space of a random experiment $\xi$ and $P$ be a probability function defined on the…

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