To find the probability [tex]\( P \)[/tex] of spinning one Red and one Green on a spinner with 4 equal sections colored purple, red, green, and blue when spun twice, we can follow these steps:
1. Determine the Probability of Each Color in a Single Spin:
- The spinner is divided into 4 equal sections, so the probability of landing on any specific color (Red, Green, Purple, or Blue) in a single spin is:
[tex]\[
\text{Probability of one color} = \frac{1}{4}
\][/tex]
2. Calculate the Probability of Spinning One Red and One Green in Two Spins:
- The probability of spinning Red first and then Green in two spins:
[tex]\[
P(\text{Red first and Green second}) = \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right)
\][/tex]
This gives:
[tex]\[
\left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) = \frac{1}{16}
\][/tex]
- The probability of spinning Green first and then Red in two spins:
[tex]\[
P(\text{Green first and Red second}) = \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right)
\][/tex]
This gives:
[tex]\[
\left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) = \frac{1}{16}
\][/tex]
3. Combine the Probabilities for Both Scenarios:
- Since either event (Red first then Green or Green first then Red) can occur, and these two events are mutually exclusive, we sum the probabilities:
[tex]\[
P(\text{One Red and One Green}) = P(\text{Red first and Green second}) + P(\text{Green first and Red second})
\][/tex]
Thus:
[tex]\[
P(\text{One Red and One Green}) = \frac{1}{16} + \frac{1}{16}
\][/tex]
Therefore:
[tex]\[
P(\text{One Red and One Green}) = \frac{1}{16} + \frac{1}{16} = \frac{2}{16} = \frac{1}{8}
\][/tex]
The probability [tex]\( P \)[/tex] of spinning one Red and one Green is [tex]\(\frac{1}{8}\)[/tex].
