Question
Use the spinner to answer the question.
A spinner, using a circle divided into 8 wedges of alternating colors, is numbered 1 to 8. The spinner arrow points to 6.
Given that the spinner lands on blue, what is the probability that it lands on an even number?
(1 point)
Responses
67%
67%
25%
25%
50%
50%
38%
38%
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A spinner, using a circle divided into 8 wedges of alternating colors, is numbered 1 to 8. The spinner arrow points to 6.
Given that the spinner lands on blue, what is the probability that it lands on an even number?
(1 point)
Responses
67%
67%
25%
25%
50%
50%
38%
38%
Remaining Attempts : 3
Skip to navigation
Answers
GPT-4o mini
To determine the probability that the spinner lands on an even number given that it lands on blue, we first need to analyze the spinner's structure.
1. The spinner is divided into 8 wedges, suggesting the numbers represented (1 to 8) cover all integers from 1 to 8.
2. On this spinner, the even numbers are 2, 4, 6, and 8—totaling 4 even numbers.
3. The odd numbers are 1, 3, 5, and 7—totaling 4 odd numbers.
Since the spinner is divided into wedges of alternating colors, it is assumed that the alternating colors (e.g., blue and another color) cover the same number of wedges. Assuming an equal distribution of colors, four of the sections will be blue, specifically for this analysis.
Given we know it landed on blue, we want to identify which of the numbers (that also are blue) are even.
If we assume the distribution of colors is two blue and two other (non-blue) for even and two blue and two other (non-blue) for odd, then:
- Blue even numbers: 2, 4 (2 outcomes)
- Blue odd numbers: 1, 3 (2 outcomes)
This implies:
- Total outcomes that are blue = 4 (2 even + 2 odd)
- Outcomes that are blue and even = 2 (2, 4)
Thus, the probability \( P \) that the spinner lands on an even number given that it landed on blue can be calculated as follows:
\[
P(\text{even | blue}) = \frac{\text{Number of blue even outcomes}}{\text{Total blue outcomes}} = \frac{2}{4} = \frac{1}{2} = 50\%
\]
Therefore, the probability that it lands on an even number given that it lands on blue is:
**50%**.
1. The spinner is divided into 8 wedges, suggesting the numbers represented (1 to 8) cover all integers from 1 to 8.
2. On this spinner, the even numbers are 2, 4, 6, and 8—totaling 4 even numbers.
3. The odd numbers are 1, 3, 5, and 7—totaling 4 odd numbers.
Since the spinner is divided into wedges of alternating colors, it is assumed that the alternating colors (e.g., blue and another color) cover the same number of wedges. Assuming an equal distribution of colors, four of the sections will be blue, specifically for this analysis.
Given we know it landed on blue, we want to identify which of the numbers (that also are blue) are even.
If we assume the distribution of colors is two blue and two other (non-blue) for even and two blue and two other (non-blue) for odd, then:
- Blue even numbers: 2, 4 (2 outcomes)
- Blue odd numbers: 1, 3 (2 outcomes)
This implies:
- Total outcomes that are blue = 4 (2 even + 2 odd)
- Outcomes that are blue and even = 2 (2, 4)
Thus, the probability \( P \) that the spinner lands on an even number given that it landed on blue can be calculated as follows:
\[
P(\text{even | blue}) = \frac{\text{Number of blue even outcomes}}{\text{Total blue outcomes}} = \frac{2}{4} = \frac{1}{2} = 50\%
\]
Therefore, the probability that it lands on an even number given that it lands on blue is:
**50%**.