Let's analyze the given problem step-by-step.
1. Understanding the Problem:
- We have a spinner with 4 equal sections.
- The sections are colored purple, red, green, and blue.
- The spinner is spun twice.
- We want to find the probability of landing on a specific color in both spins.
2. Step-by-Step Calculation:
- First, determine the probability of landing on a specific color in a single spin. Since there are 4 equal sections, the probability of landing on any specific color (like purple) in one spin is:
[tex]\[
\text{Probability in one spin} = \frac{1}{4}
\][/tex]
- Next, we need to find the combined probability for two spins. The events (spins) are independent, so the combined probability of landing on a specific color in both spins is obtained by multiplying the probabilities of each individual spin:
[tex]\[
\text{Combined Probability} = \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right)
\][/tex]
- Simplifying this, we get:
[tex]\[
\left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) = \frac{1}{16}
\][/tex]
3. Conclusion:
- The probability of landing on a specific color in both spins is [tex]\(\frac{1}{16}\)[/tex].
Therefore, the correct answer is [tex]\(\frac{1}{16}\)[/tex].
