Question
Bivariate Data Analysis & Probability Unit Test
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Question
Use the image to answer the question.
An illustration of a circle with eight equal parts labeled from 1 through 8 clockwise. An arrow starting in part 1 passes through the center to point into part 5.
The spinner is spun twice. What is the probability that the spinner lands on both multiples of 4 in both spins?
(1 point)
Responses
14
Start Fraction 1 over 4 End Fraction
132
Start Fraction 1 over 32 End Fraction
116
Start Fraction 1 over 16 End Fraction
364
Start Fraction 3 over 64 End Fraction
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Answers
GPT-4o mini
To find the probability that the spinner lands on both multiples of 4 in both spins, let's first identify the multiples of 4 on the spinner.
The numbers on the spinner are 1, 2, 3, 4, 5, 6, 7, and 8. The multiples of 4 within this range are:
- 4
- 8
Therefore, there are 2 multiples of 4 on the spinner.
Since the spinner is spun twice, we will calculate the probability of landing on a multiple of 4 for both spins. The probability of landing on a multiple of 4 in one spin is:
\[
\text{Probability of landing on a multiple of 4} = \frac{\text{Number of multiples of 4}}{\text{Total numbers on the spinner}} = \frac{2}{8} = \frac{1}{4}
\]
Since the spins are independent, the probability of landing on a multiple of 4 in both spins is:
\[
\text{Probability for both spins} = \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) = \frac{1}{16}
\]
Therefore, the probability that the spinner lands on both multiples of 4 in both spins is:
\[
\frac{1}{16}
\]
The correct response is:
**Start Fraction 1 over 16 End Fraction**
The numbers on the spinner are 1, 2, 3, 4, 5, 6, 7, and 8. The multiples of 4 within this range are:
- 4
- 8
Therefore, there are 2 multiples of 4 on the spinner.
Since the spinner is spun twice, we will calculate the probability of landing on a multiple of 4 for both spins. The probability of landing on a multiple of 4 in one spin is:
\[
\text{Probability of landing on a multiple of 4} = \frac{\text{Number of multiples of 4}}{\text{Total numbers on the spinner}} = \frac{2}{8} = \frac{1}{4}
\]
Since the spins are independent, the probability of landing on a multiple of 4 in both spins is:
\[
\text{Probability for both spins} = \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) = \frac{1}{16}
\]
Therefore, the probability that the spinner lands on both multiples of 4 in both spins is:
\[
\frac{1}{16}
\]
The correct response is:
**Start Fraction 1 over 16 End Fraction**