Sure! Let's solve this step-by-step.
1. Determine the total number of slips:
There are 24 slips, each with a unique number from 1 to 24.
2. Identify the numbers that are divisible by 3 within this range:
The numbers divisible by 3 between 1 and 24 are: 3, 6, 9, 12, 15, 18, 21, and 24.
3. Count the numbers divisible by 3:
There are 8 numbers in total that are divisible by 3.
4. Calculate the numbers not divisible by 3:
To find the numbers that are not divisible by 3, subtract the count of numbers divisible by 3 from the total number:
[tex]\[
24 - 8 = 16
\][/tex]
So, there are 16 numbers that are not divisible by 3.
5. Find the probability of selecting a number that is not divisible by 3:
The probability of selecting such a number is the ratio of the number of favorable outcomes (numbers not divisible by 3) to the total number of outcomes (total slips of paper). Therefore:
[tex]\[
\text{Probability} = \frac{\text{Number of not divisible by 3}}{\text{Total number of slips}} = \frac{16}{24}
\][/tex]
6. Simplify the fraction:
Simplify [tex]\(\frac{16}{24}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (which is 8):
[tex]\[
\frac{16}{24} = \frac{16 \div 8}{24 \div 8} = \frac{2}{3}
\][/tex]
So, the probability that you will select a number not divisible by 3 is [tex]\(\frac{2}{3}\)[/tex].
Thus, the correct answer is:
[tex]\(\boxed{\frac{2}{3}}\)[/tex]
