Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability of a number which is a perfect cube.
Perfect cubes in your domain:
8, 27, 64
number of cards : 100
prob(cube) = 3/100
To find the probability of drawing a number which is a perfect cube, we need to calculate the number of perfect cube numbers between 2 and 101 and divide it by the total number of cards in the box.
Step 1: Determine the perfect cube numbers between 2 and 101.
The perfect cube numbers between 2 and 101 are 8, 27, and 64.
Step 2: Calculate the total number of cards in the box.
The total number of cards in the box is 100 (from 2 to 101), excluding the 1 card.
Step 3: Calculate the probability.
The probability of drawing a perfect cube number is the number of perfect cube numbers divided by the total number of cards.
In this case, the probability is 3 (number of perfect cube numbers) divided by 100 (total number of cards) = 3/100 = 0.03 or 3%.
Therefore, the probability of drawing a number which is a perfect cube is 3%.