To find the probability that a randomly selected card does not have a 5 or a 2, we first need to count the total number of cards and how many of those do not have a 5 or a 2.
The numbers on the cards are: 5, 3, 6, 2, 2, 5, 6, 5, 8.
Let's count the total number of cards:
- Total number of cards = 9
Next, let's identify the cards that are either 5 or 2:
- The 5's in the list are: 5, 5, 5 (which is 3 occurrences)
- The 2's in the list are: 2, 2 (which is 2 occurrences)
Now, let's find the total occurrences of the numbers we want to exclude (5's and 2's):
- Total occurrences of 5 and 2 = 3 (for 5) + 2 (for 2) = 5
Now, we can find the number of cards that do not have a 5 or a 2:
- Cards that do not have a 5 or 2 = Total cards - Cards that have a 5 or 2 = 9 - 5 = 4
The numbers remaining, after excluding 5's and 2's, are: 3, 6, 6, 8.
Finally, we can calculate the probability:
- Probability = (Number of favorable outcomes) / (Total number of outcomes)
- Probability = 4 / 9
Therefore, the probability that a randomly selected card does not have a 5 or a 2 is \( \frac{4}{9} \).