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Mathematics

Assertion (A): If the probability of occurrence of an event E is 511\dfrac{5}{11}, then the probability of non-occurrence of the event E is 711\dfrac{7}{11}.

Reason (R): If E is an event, then P(E) + P(E\overline{E}) = 1.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Probability

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Answer

Given, the probability of occurrence of an event E = 511\dfrac{5}{11}

As we know that the sum of probabilities of two complementary event is 1.

⇒ P(E) + P(E\overline{E}) = 1

∴ Reason (R) is true.

511+P(E)=1P(E)=1511P(E)=11511P(E)=611\Rightarrow \dfrac{5}{11} + P(\overline{E}) = 1\\[1em] \Rightarrow P(\overline{E}) = 1 - \dfrac{5}{11}\\[1em] \Rightarrow P(\overline{E}) = \dfrac{11 - 5}{11}\\[1em] \Rightarrow P(\overline{E}) = \dfrac{6}{11}

∴ Assertion (A) is false.

∴ Assertion (A) is false, but Reason (R) is true.

Hence, option 2 is the correct option.

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