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Mathematics

Assertion (A): Two players Sania and Asma play a tennis match. If the probability of Sania winning the match is 0.79, then the probability of Asma winning the match is 0.21.

Reason (R): The sum of probabilities of two complementary event is 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 Sania winning the match = 0.79.

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

⇒ P(Sania wins) + P(Asma wins) = 1

∴ Reason (R) is true.

⇒ 0.79 + P(Asma wins) = 1

⇒ P(Asma wins) = 1 - P(Sania wins)

⇒ P(Asma wins) = 1 - 0.79

⇒ P(Asma wins) = 0.21

∴ Assertion (A) is true.

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

Hence, option 3 is the correct option.

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