GATE CS 2020 Set 1 — Question 55
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Engineering Mathematics → Probability & Statistics → Sample Space & Events
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Question
For , let be a non-zero vector. Suppose that is chosen uniformly at random from . Then, the probability that is an odd number is _______.
Correct answer
0.5 to 0.5
Solution
We are looking for the probability that the dot product .
1.Since is a non-zero vector, there exists at least one index such that .
2.The sum can be written as: .
3.Let . Then (since ).
4. is chosen uniformly at random, meaning each is independently 0 or 1 with probability 0.5.
5.Regardless of the value of (determined by for ), the value of depends on :
- If is even, is odd if .
- If is odd, is odd if .
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