TS EAMCET · Maths · Probability
If a number \(x\) is drawn randomly from the set of numbers \(\{1,2,3, \ldots, 50\}\), then the probability that number \(x\) that is drawn satisfies the inequation \(x+\frac{10}{x} \leq 11\) is
- A \(\frac{4}{5}\)
- B \(\frac{9}{50}\)
- C \(\frac{4}{25}\)
- D \(\frac{1}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{5}\)
Step-by-step Solution
Detailed explanation
\(x+\frac{10}{x} \leq 11\) \(x^2+10 \leq 11x\) \(x^2-11x+10 \leq 0\) \((x-1)(x-10) \leq 0\) \(1 \leq x \leq 10\) Favorable numbers: \(\{1,2,3,4,5,6,7,8,9,10\}\) Number of favorable outcomes = \(10\) Total number of outcomes = \(50\) Probability = \(\frac{10}{50} = \frac{1}{5}\)
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