Question

1. the following venn diagram is the result of asking the first 50 customers at a food truck if they like ketchup, mustard, or both. use the venn diagram to answer the following questions.

a. how many people say they like mustard?
b. how many people like ketchup and mustard?
c. how many people like ketchup or mustard?

Explanation:

Step1: Identify the number for mustard - only and both

The number of people who like only mustard is 8 and the number of people who like both ketchup and mustard is 10.

Step2: Calculate the number of people who like mustard

To find the number of people who like mustard, we add the number of people who like only mustard and the number of people who like both. So, \(8 + 10=18\).

Step3: Calculate the number of people who like both ketchup and mustard

The number of people who like both ketchup and mustard is directly given in the intersection of the Venn - diagram as 10.

Step4: Calculate the number of people who like ketchup or mustard

We use the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), where \(A\) is the set of people who like ketchup and \(B\) is the set of people who like mustard. Here, \(n(A) = 32+10\), \(n(B)=8 + 10\), and \(n(A\cap B)=10\). So \(n(A\cup B)=(32 + 10)+(8 + 10)-10=50\).

Answer:

a. 18
b. 10
c. 50