In a bag there are three balls , one red , one blue and one yellow. A ball is selected ,the colour is recorded and the ball is replaced. A second ball is then selected and the colour is recorded.
Show in a tree diagam all the possible combined outcomes .

Answer

To solve the problem, we need to create a tree diagram that shows all the possible combined outcomes when selecting two balls from a bag containing one red ball, one blue ball, and one yellow ball.

### Step-by-step Solution:

1. **Identify the First Selection:**
- The first ball can be one of the following colors:
- Red (R)
- Blue (B)
- Yellow (Y)

2. **Draw the First Level of the Tree:**
- Start with a single point (the root) and draw three branches from it, representing the three possible outcomes of the first selection:
- R (Red)
- B (Blue)
- Y (Yellow)

3. **Identify the Second Selection:**
- After the first ball is selected and recorded, it is replaced. Therefore, the second ball can again be one of the following colors:
- Red (R)
- Blue (B)
- Yellow (Y)

4. **Draw the Second Level of the Tree:**
- From each of the outcomes of the first selection (R, B, Y), draw three branches representing the possible outcomes of the second selection:
- From R: R, B, Y
- From B: R, B, Y
- From Y: R, B, Y

5. **List All Combined Outcomes:**
- The combined outcomes from the tree diagram will be:
- (R, R)
- (R, B)
- (R, Y)
- (B, R)
- (B, B)
- (B, Y)
- (Y, R)
- (Y, B)
- (Y, Y)

### Final Tree Diagram Representation:
```
Start
/ | \
R B Y
/|\ /|\ /|\
R B Y R B Y
```

### Combined Outcomes:
- (R, R)
- (R, B)
- (R, Y)
- (B, R)
- (B, B)
- (B, Y)
- (Y, R)
- (Y, B)
- (Y, Y)