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AP EAMCET · Maths · Probability

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 \(\mathrm{E}_1 \subseteq \mathrm{E}_2 \mathrm{P}\left(\mathrm{E}_2\right) \leq \mathrm{P}\left(\mathrm{E}_1\right)\)

  1. A (iii)
  2. B (iv)
  3. C (ii)
  4. D (i)
Verified Solution

Answer & Solution

Correct Answer

(B) (iv)

Step-by-step Solution

Detailed explanation

If \(E_1 \subseteq E_2\) Then \(P\left(E_1\right) \leq P\left(E_2\right)\) \(\therefore\) Statement (iv) is not satisfied by \(P\)