Numbers from 3 to 51 are placed in a box. If a number is drawn from it, find the probability that the number drawn is a perfect cube.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{2}{49}\)
Probability = number of favourable outcomes ÷ total number of outcomes, each number in the box being equally likely to be drawn.
Numbers from 3 to 51: \(51-3+1=49\) numbers
Perfect cubes among them: \(2^3=8\) and \(3^3=27\) (the next cube, 64, is too big, and 1 is below 3), so 2 cubes
Probability \(\displaystyle =\frac{2}{49}\)