To determine the probability of spinning one Green and one Blue when a spinner with 3 equal sections (orange, green, and blue) is spun twice, follow these steps:
1. Identify the individual probabilities of each color:
- Since the spinner has 3 equal sections, the probability of landing on any one section in a single spin is [tex]\(\frac{1}{3}\)[/tex].
2. Find the probability of spinning Green in one spin:
- The probability is [tex]\(\frac{1}{3}\)[/tex].
3. Find the probability of spinning Blue in one spin:
- Similarly, the probability is [tex]\(\frac{1}{3}\)[/tex].
4. Calculate the probability of spinning one Green and one Blue in two spins:
- There are two favorable outcomes:
- First spin Green and second spin Blue.
- First spin Blue and second spin Green.
- The probability of the first scenario (Green followed by Blue) is:
[tex]\[
P(\text{Green then Blue}) = \left(\frac{1}{3}\right) \times \left(\frac{1}{3}\right) = \frac{1}{9}
\][/tex]
- The probability of the second scenario (Blue followed by Green) is:
[tex]\[
P(\text{Blue then Green}) = \left(\frac{1}{3}\right) \times \left(\frac{1}{3}\right) = \frac{1}{9}
\][/tex]
- Adding these probabilities to account for both favorable sequences:
[tex]\[
P(\text{one Green and one Blue}) = \frac{1}{9} + \frac{1}{9} = \frac{2}{9}
\][/tex]
Thus, the probability [tex]\(P\)[/tex] of spinning one Green and one Blue in two spins is [tex]\(\frac{2}{9}\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{\frac{2}{9}}
\][/tex]
