Gate2020 cs Q49

0. For n > 2, let a ∈ {0, 1}ⁿ be a non-zero vector. Suppose that x is chosen uniformly at random form (0,1)n. Then, the probability that Gate2020 cs is an number is _______ .

Note – Numerical Type question

Answer
Comment
Array

Option : A
Explanation :
Let n = 3
0 ϵ < 0,1]³

x = 0 or 1

= x₁ = x₃ (∵ a₁ = 1, a₂= 0, a₃ = 1)
= 0 or 1 or 1 or 2.

= x₃ (∵ a₁ = a₂ = 0)
= 0 or 1

Total number of cases = 2 × 3 + 4 × 3 = 18
Now odd number of cases = 9
P = 9/18 = 0.5

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