A sample of 3 bulbs is tested. A bulb is labelled 'G' if it is good and 'D' if it defective. Find the number of all the possible outcomes.

Answer

To find the number of all possible outcomes when testing a sample of 3 bulbs, where each bulb can either be good (G) or defective (D), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Choices for Each Bulb**:
Each bulb can be in one of two states: Good (G) or Defective (D).

2. **Determine the Number of Bulbs**:
We have a total of 3 bulbs.

3. **Calculate the Total Outcomes**:
For each bulb, there are 2 choices (G or D). Since the choices are independent for each bulb, we can use the multiplication principle of counting.
Therefore, the total number of outcomes can be calculated as:
\[ \text{Total Outcomes} = 2^{\text{Number of Bulbs}} = 2^3 \]

4. **Perform the Calculation**:
\[ 2^3 = 8 \]

5. **List All Possible Outcomes**:
The possible outcomes can be listed as follows:
- GGG (all good)
- GGD (two good, one defective)
- GDG (two good, one defective)
- DGG (two good, one defective)
- GDD (one good, two defective)
- DGD (one good, two defective)
- DDG (one good, two defective)
- DDD (all defective)

6. **Conclusion**:
Therefore, the total number of all possible outcomes when testing the 3 bulbs is 8.

### Final Answer:
The number of all possible outcomes is **8**.

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