A manufacturer of television sets trims sets in either black or grey and uses either a walnut or a maple stain. A consumer survey showed that 20% of consumers wanted a black trim with a walnut stain and that half of all consumers wanted a black trim or a walnut stain. If it has already been decided to trim 30% of the sets in black, what proportion of the sets should be given a walnut stain?
To find the proportion of sets that should be given a walnut stain, we need to analyze the information given.
Let's start by breaking down the information we have:
1. 20% of consumers wanted a black trim with a walnut stain.
2. Half of all consumers wanted a black trim or a walnut stain.
3. It has already been decided to trim 30% of the sets in black.
From this information, we can deduce that the proportion of consumers who want a walnut stain is half of all consumers minus the proportion of consumers who want a black trim with a walnut stain.
Let's calculate it step by step:
1. Calculate the proportion of consumers who want a black trim or a walnut stain:
- This is given as half of all consumers, so it is 0.5.
2. Calculate the proportion of consumers who want a black trim with a walnut stain:
- This is given as 20% of consumers, so it is 0.2.
3. Calculate the proportion of consumers who only want a walnut stain:
- This is the difference between the proportion of consumers who want a black trim or a walnut stain (0.5) and the proportion of consumers who want a black trim with a walnut stain (0.2):
- 0.5 - 0.2 = 0.3
Therefore, the proportion of sets that should be given a walnut stain is 0.3.