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A number x is randomly selected from the first 100 positive integers. What is the probability that the inequality (x² - 60x + 800) / (x - 30) < 0 holds true?
- 3 out of 50
- 1 out of 50
- 7 out of 25
- 3 out of 50
Correct answer: 7 out of 25
Solution
The inequality given can be simplified and solved to find the range of x values for which it holds true, and then the probability can be calculated based on the number of integers within this range out of the total 100 positive integers, leading to the probability of 7 out of 25.
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