Question

Consider a spinner that has the numbers 1–8. What is the probability of getting a number greater than 3 or an even number? Write your answer as a reduced fraction.(1 point)
Responses

516
5
16
5 over 16 - no response given

34
3
4
3 fourths - no response given

98
9
8
9 eighths - no response given

38

Answer 1

To find the probability of getting a number greater than 3 or an even number on a spinner numbered from 1 to 8, we can use the principle of inclusion-exclusion.

1. **Identify the outcomes**:
The possible outcomes of the spinner are:
{1, 2, 3, 4, 5, 6, 7, 8}

2. **Numbers greater than 3**:
The numbers greater than 3 are:
{4, 5, 6, 7, 8}
This gives us 5 favorable outcomes.

3. **Even numbers**:
The even numbers are:
{2, 4, 6, 8}
This gives us 4 favorable outcomes.

4. **Numbers that are both greater than 3 and even**:
The even numbers greater than 3 are:
{4, 6, 8}
This gives us 3 favorable outcomes.

5. **Applying inclusion-exclusion**:
The total number of favorable outcomes for getting a number greater than 3 or an even number can be found using the formula:
\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]
Where:
- \( P(A) \) is the number of outcomes greater than 3 (5 outcomes).
- \( P(B) \) is the number of even numbers (4 outcomes).
- \( P(A \cap B) \) is the number of outcomes that are both greater than 3 and even (3 outcomes).

Thus:
\[
P(A \cup B) = 5 + 4 - 3 = 6
\]

6. **Total possible outcomes**:
There are 8 possible outcomes on the spinner.

7. **Calculating probability**:
The probability of getting a number greater than 3 or an even number is:
\[
P(A \cup B) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{8}
\]

8. **Reducing the fraction**:
The fraction \(\frac{6}{8}\) can be simplified:
\[
\frac{6}{8} = \frac{3}{4}
\]

Therefore, the final answer for the probability of getting a number greater than 3 or an even number is:

\[\frac{3}{4}\] or \(3\) fourths.