An integer number is chosen at random from the first 100 integers. What is the probability that the chosen number is a perfect cube?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1/25
The probability of an event is the number of favourable outcomes divided by the total number of outcomes. The first 100 integers are 1 to 100, so there are 100 equally likely outcomes.
Perfect cubes up to 100: \(1^3=1\), \(2^3=8\), \(3^3=27\), \(4^3=64\); the next one, \(5^3=125\), is too big
Favourable outcomes: 4
Probability \(\displaystyle =\frac{4}{100}=\frac{1}{25}\)