A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies x+\frac{1}{x} \gt 2?
- A. \frac{1}{n}
- B. \frac{1}{(2n)}
- C. \frac{(n-1)}{n} ✓
- D. 1
Correct Answer: C. \frac{(n-1)}{n}
Explanation
The inequality x + \frac{1}{x} \gt 2 is true for all positive real numbers x except x=1, where 1 + 1 = 2. Out of the first n natural numbers, exactly n-1 numbers satisfy this condition. Therefore, the probability is \frac{n-1}{n}.
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