To find the probability that a randomly customized chess set will have abstract pieces made of either glass or wood, we'll first determine the total number of possible combinations of materials and styles.
Step 1: Count the Options
- Materials: 5 options (Glass, Resin, Steel, Stone, Wood)
- Styles: 4 options (Abstract, Classic, Mesoamerican, Fantasy)
Step 2: Calculate the Total Combinations
The total number of combinations can be calculated by multiplying the number of options for materials by the number of options for styles: \[ \text{Total Combinations} = \text{Number of Materials} \times \text{Number of Styles} = 5 \times 4 = 20 \]
Step 3: Identify Favorable Outcomes
Next, we identify the favorable outcomes. We want the chess sets that are:
- Abstract style
- Made from either Glass or Wood
The possibilities that satisfy these conditions are:
- Abstract style with Glass material
- Abstract style with Wood material
This gives us a total of 2 favorable combinations:
- Abstract & Glass
- Abstract & Wood
Step 4: Calculate the Probability
Now we can calculate the probability of having abstract pieces made of either glass or wood: \[ P(\text{Abstract and Glass or Wood}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Combinations}} = \frac{2}{20} = \frac{1}{10} \]
Thus, the probability that the chess set will have abstract pieces made of either glass or wood is:
\[ \boxed{\frac{1}{10}} \]
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