A natural number x is chosen at random from the first 100 natural numbers. What is the probability that x^{2}+x \gt 50?

Explanation

The inequality is x(x+1) \gt 50. Testing integers starting from 1: for x=6, 6(7) = 42 \ngtr 50. For x=7, 7(8) = 56 \gt 50. The inequality holds for all integers from x=7 to x=100. Out of 100 numbers, exactly 6 fail the condition, leaving 94 numbers that satisfy it. The probability is \frac{94}{100} = \frac{47}{50}.

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