Let 𝑀 be a randomly chosen non-empty subset of 𝑆 = {1,2,3,…,2026}. Which of…

GATE Β· 2026 Β· DA Β· Data Science & AI

Let 𝑀 be a randomly chosen non-empty subset of 𝑆 = {1,2,3,…,2026}. Which of the following is the probability that the product of all the elements of 𝑀 is even?

  1. A.

    21013(21013 βˆ’ 1)/22026

  2. B.

    2101322026\frac{2^{1013}}{2^{2026}}

  3. C.

    21013(21013 βˆ’ 1)/(22026 βˆ’ 1)

  4. D.

    1/(22026 βˆ’ 1)

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