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 ,
no match is lost ,

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 calculate the probability that no match is lost.

### Step 1: Draw the Tree Diagram

1. **First Match Outcomes**: The first match can result in one of three outcomes:
- Win (W)
- Draw (D)
- Lose (L)

2. **Second Match Outcomes**: For each outcome of the first match, the second match can also result in:
- Win (W)
- Draw (D)
- Lose (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 possible outcomes of the two matches:
1. WW (Win, Win)
2. WD (Win, Draw)
3. WL (Win, Lose)
4. DW (Draw, Win)
5. DD (Draw, Draw)
6. DL (Draw, Lose)
7. LW (Lose, Win)
8. LD (Lose, Draw)
9. LL (Lose, Lose)

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

### Step 3: Calculate the Probability that No Match is Lost

Next, we need to find the outcomes where no match is lost. The outcomes that satisfy this condition are:
1. WW (Win, Win)
2. WD (Win, Draw)
3. DW (Draw, Win)
4. DD (Draw, Draw)

These outcomes are:
- WW
- WD
- DW
- DD

Now, we count the number of favorable outcomes:
- Number of favorable outcomes = 4

Total number of outcomes in the sample space = 9

### Step 4: Calculate the Probability

The probability (P) that no match is lost is given by the formula:
\[ P(\text{No match lost}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values:
\[ P(\text{No match lost}) = \frac{4}{9} \]

### Final Answer

The probability that no match is lost is \( \frac{4}{9} \).

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