Questions: A drug company is testing new toothpaste in two flavors, regular and cinnamon. In a sample of 152 people, 87 liked regular, 73 people liked cinnamon, and 20 liked both. Of those sampled, how many liked only the regular? Of those sampled, how many liked only cinnamon? Of those sampled, how many liked either one or the other or both? Of those sampled, how many liked neither?

A drug company is testing new toothpaste in two flavors, regular and cinnamon. In a sample of 152 people, 87 liked regular, 73 people liked cinnamon, and 20 liked both.

Of those sampled, how many liked only the regular?
Of those sampled, how many liked only cinnamon?
Of those sampled, how many liked either one or the other or both?
Of those sampled, how many liked neither?
Transcript text: A drug company is testing new toothpaste in two flavors, regular and cinnamon. In a sample of 152 people, 87 liked regular, 73 people liked cinnamon, and 20 liked both. Of those sampled, how many liked only the regular? $\square$ Of those sampled, how many liked only cinnamon? $\square$ Of those sampled, how many liked either one or the other or both? $\square$ Of those sampled, how many liked neither? $\square$
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Solution

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Solution Steps

Step 1: Identify the given values
  • Total number of people sampled (U) = 152
  • Number of people who liked regular toothpaste (A) = 87
  • Number of people who liked cinnamon toothpaste (B) = 73
  • Number of people who liked both regular and cinnamon toothpaste (A ∩ B) = 20
Step 2: Calculate the number of people who liked only regular toothpaste
  • Number of people who liked only regular toothpaste (A - A ∩ B) = 87 - 20 = 67
Step 3: Calculate the number of people who liked only cinnamon toothpaste
  • Number of people who liked only cinnamon toothpaste (B - A ∩ B) = 73 - 20 = 53

Final Answer

  1. Number of people who liked only regular toothpaste: 67
  2. Number of people who liked only cinnamon toothpaste: 53
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