Question:

If a number is chosen at random from the set \( \{1, 2, 3, \dots, 100\} \), then the probability that it is a perfect cube is:

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Perfect Powers in a Range}
Use \( n^3 \leq 100 \) to count perfect cubes
Always divide count by total number of elements
Don’t mistake squares for cubes
Updated On: May 19, 2025
  • \( \frac{1}{25} \)
  • \( \frac{1}{2} \)
  • \( \frac{1}{10} \)
  • \( \frac{9}{13} \)
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The Correct Option is A

Solution and Explanation

Perfect cubes between 1 and 100 are: \[ 1^3 = 1,\quad 2^3 = 8,\quad 3^3 = 27,\quad 4^3 = 64 \Rightarrow 4 \text{ numbers} \] Total numbers = 100 \[ P(\text{perfect cube}) = \frac{4}{100} = \frac{1}{25} \]
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