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.
or, count the cubes: 8,27,64
oops 😳 🙁 😔 😔
To find the probability of drawing a number that is a perfect cube, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Let's break down the problem step by step:
Step 1: Determine the total number of possible outcomes.
We are drawing one card from a box that contains cards marked with numbers from 2 to 101. Hence, there are 101 cards in total.
Step 2: Determine the number of favorable outcomes.
We want to find the probability of drawing a perfect cube number. Perfect cubes are numbers that can be obtained by multiplying an integer by itself twice (e.g., 1 * 1 * 1 = 1, 2 * 2 * 2 = 8). There are 5 perfect cube numbers in the given range (2, 8, 27, 64, 125). However, since we only have cards numbered from 2 to 101, we need to exclude the number 125, as it is outside the range. So we have 4 favorable outcomes.
Step 3: Calculate the probability.
The probability (P) is given by the formula:
P = (Number of favorable outcomes) / (Total number of possible outcomes)
Therefore, the probability of drawing a number that is a perfect cube is:
P = 4 / 101
That simplifies to:
P ≈ 0.0396 or 3.96%
So, the probability of drawing a number that is a perfect cube is approximately 0.0396 or 3.96%.
cards from 1 to 101 would be 101
so cards from 2 to 101 is 100
list of primes between 2 and 101 :
4,9,16,25,36,49,64,81,100
count the perfect squares
finish it up