To solve this problem, we need to determine the probability that the pointer lands on either an even number or a number greater than 5.

Step 1: List the numbers on the spinner.

The spinner is numbered 1 through 8.
The numbers are:
$1, 2, 3, 4, 5, 6, 7, 8$

Step 2: Identify the favorable outcomes.

We are interested in numbers that satisfy either:

1. Even numbers: Numbers divisible by 2 → 2, 4, 6, 8
2. Numbers greater than 5: These numbers are 6, 7, 8.

Now, combine these two sets while avoiding double-counting:

• Even numbers: 2, 4, 6, 8
• Numbers greater than 5: 6, 7, 8

Combining these, the unique favorable outcomes are:
$2, 4, 6, 7, 8$

Step 3: Count the favorable outcomes.

From the list above, the favorable outcomes are:
$2, 4, 6, 7, 8$ → Total = 5 outcomes.

Step 4: Determine the total outcomes.

The spinner has 8 equal regions, so the total number of possible outcomes is 8.

Step 5: Calculate the probability.

The probability is given by:
$P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Substitute the values:
$P = \frac{5}{8}$

Final Answer:

The probability is 5/8.

Would you like a detailed explanation of any step or further clarification?

Here are 5 related questions for further practice:

1. What is the probability of landing on an odd number?
2. What is the probability of landing on a number less than 4?
3. What is the probability of landing on an even number and greater than 5?
4. If the spinner is spun twice, what is the probability of landing on 8 both times?
5. What is the probability of landing on a prime number?

Tip: Always identify and list favorable outcomes carefully when solving probability questions.