A match can be won , drawn or lost One week a school it to play two matches .Draw a tree diagram to show all the possible outcomes and list them . If the outcomes are equally likely ,calculate the probability that ,
both matches are won ,

Answer

To solve the problem step-by-step, we will first draw a tree diagram to represent all possible outcomes of the two matches, and then we will calculate the probability of both matches being won.

### Step 1: Draw the Tree Diagram

1. **First Match Outcomes**: The first match can have three outcomes:
- Won (W)
- Drawn (D)
- Lost (L)

2. **Second Match Outcomes**: For each outcome of the first match, the second match can also have three outcomes:
- Won (W)
- Drawn (D)
- Lost (L)

Now, we can represent this in a tree diagram:

```
Match 1
/ | \
W D L
/|\ /|\ /|\
W D L W D L W D L
```

### Step 2: List All Possible Outcomes

From the tree diagram, we can list all the possible outcomes for the two matches:

1. WW (Won, Won)
2. WD (Won, Drawn)
3. WL (Won, Lost)
4. DW (Drawn, Won)
5. DD (Drawn, Drawn)
6. DL (Drawn, Lost)
7. LW (Lost, Won)
8. LD (Lost, Drawn)
9. LL (Lost, Lost)

So, the complete sample space is:
- { WW, WD, WL, DW, DD, DL, LW, LD, LL }

### Step 3: Calculate the Probability of Both Matches Being Won

1. **Total Outcomes**: There are 9 outcomes in total.
2. **Favorable Outcomes**: The only favorable outcome for both matches being won is:
- WW

Thus, there is only 1 favorable outcome.

3. **Probability Calculation**:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{1}{9} \]

### Final Answer
The probability that both matches are won is \( \frac{1}{9} \).

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