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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Probability

NDA 2024 · Mathematics · Probability

A natural number x is chosen at random from the first 100 natural...

A natural number xx is chosen at random from the first 100 natural numbers. What is the probability that x2+x>50x^2+x > 50 ?

Options

  1. A93100\frac{93}{100}
  2. B4750\frac{47}{50}
  3. C2425\frac{24}{25}
  4. D2325\frac{23}{25}

Correct answer

B. 4750\frac{47}{50}

Step-by-step solution

First 100 natural numbers n(s)=100\mathrm{n}(\mathrm{ s})=100 Number from 7 to 100 satisfy x2+x>50∴n(E)=100−6=94P(E)=n(E)n(S)=94100=4750\begin{aligned} & x^2+x > 50 \\ & \therefore \quad n(E)=100-6=94 \\ & P(E)=\frac{n(E)}{n(S)}=\frac{94}{100}=\frac{47}{50} \end{aligned}
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