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A market research group conducted a survey of consumers and reported that consumers liked the product and consumers liked product B. What is the least number that must have liked both products?
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Q. A market research group conducted a survey of consumers and reported that consumers liked the product and consumers liked product B. What is the least number that must have liked both products?
- Formulate Principle: We need to find the minimum overlap between the two groups of consumers who liked products A and B.This is a classic application of the principle of inclusion-exclusion.The formula for the principle of inclusion-exclusion is:Number liking both A and B = (Number liking A) + (Number liking B) - (Total number surveyed)
- Plug in Numbers: First, let's plug in the numbers we know into the formula:Number liking both A and B = (liking A) + (liking B) - (total surveyed)
- Perform Calculation: Now, let's do the calculation:Number liking both A and B = Number liking both A and B = Number liking both A and B =
- Determine Minimum Number: The least number that must have liked both products is therefore . This is because if more than liked both, the total number of consumers would exceed when adding those who liked only one product.
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