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
38%
38%
67%
67%
50%
50%
25%
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
38%
38%
67%
67%
50%
50%
25%
Answers
GPT-4o mini
To find the probability that the spinner lands on an even number given that it lands on blue, we first need to identify the even numbers and the colored wedges.
The numbers on the spinner are 1, 2, 3, 4, 5, 6, 7, and 8. The even numbers among these are 2, 4, 6, and 8.
Since the spinner is divided into 8 wedges of alternating colors, let's assume the colors are distributed in such a way that half of the even numbers are blue. This is a common setup in problems involving spinners.
If we assume that 2, 4, 6, and 8 are evenly distributed between blue and the other color (let's say red), we might have, for instance:
- Blue: 2, 4
- Red: 1, 3, 5, 6, 7, 8
However, we can also assume a situation where only some of the even numbers are blue. To keep it simple, if we assume that out of four even numbers (2, 4, 6, 8), two of them are blue (2 and 4, for instance).
Thus, if we consider the even numbers only:
- Even numbers: 2, 4, 6, 8 (total of 4 even numbers)
- Assuming blue even numbers: 2, 4 (total of 2 blue even numbers)
So, if we say the number of blue outcomes is 2 (2 and 4 being the blue numbers), then the total number of blue numbers would be the count of blue outcomes among all outcomes.
Now, the conditional probability formula is used here:
\[ P(Even | Blue) = \frac{P(Even \cap Blue)}{P(Blue)} \]
With:
- \( P(Even \cap Blue) = \text{Number of Blue Even Outcomes} = 2 \)
- \( P(Blue) = \text{Total Blue} \) (assumed as 4 total blue numbers in this simple setup example)
Assuming that exactly half of the outcomes are blue (4 out of 8), then:
\[ P(Blue) = 4 \]
Putting this together:
- There are 2 even blue numbers out of 4 blue outcomes.
- Thus:
\[ P(Even | Blue) = \frac{2}{4} = \frac{1}{2} = 50\% \]
The final answer is:
**50%**
The numbers on the spinner are 1, 2, 3, 4, 5, 6, 7, and 8. The even numbers among these are 2, 4, 6, and 8.
Since the spinner is divided into 8 wedges of alternating colors, let's assume the colors are distributed in such a way that half of the even numbers are blue. This is a common setup in problems involving spinners.
If we assume that 2, 4, 6, and 8 are evenly distributed between blue and the other color (let's say red), we might have, for instance:
- Blue: 2, 4
- Red: 1, 3, 5, 6, 7, 8
However, we can also assume a situation where only some of the even numbers are blue. To keep it simple, if we assume that out of four even numbers (2, 4, 6, 8), two of them are blue (2 and 4, for instance).
Thus, if we consider the even numbers only:
- Even numbers: 2, 4, 6, 8 (total of 4 even numbers)
- Assuming blue even numbers: 2, 4 (total of 2 blue even numbers)
So, if we say the number of blue outcomes is 2 (2 and 4 being the blue numbers), then the total number of blue numbers would be the count of blue outcomes among all outcomes.
Now, the conditional probability formula is used here:
\[ P(Even | Blue) = \frac{P(Even \cap Blue)}{P(Blue)} \]
With:
- \( P(Even \cap Blue) = \text{Number of Blue Even Outcomes} = 2 \)
- \( P(Blue) = \text{Total Blue} \) (assumed as 4 total blue numbers in this simple setup example)
Assuming that exactly half of the outcomes are blue (4 out of 8), then:
\[ P(Blue) = 4 \]
Putting this together:
- There are 2 even blue numbers out of 4 blue outcomes.
- Thus:
\[ P(Even | Blue) = \frac{2}{4} = \frac{1}{2} = 50\% \]
The final answer is:
**50%**