Question

a survey asked 100 people what kind of ice cream they prefer. 55 people like vanilla ice cream, 50 people liked chocolate ice cream, and 5 did not like vanilla or chocolate. how many people liked both vanilla and chocolate ice cream

Answer 1

By applying the principle of inclusion-exclusion to the survey data, it is determined that 5 people liked both vanilla and chocolate ice cream.

Step-by-step explanation:

To find out how many people liked both vanilla and chocolate ice cream, we can use the principle of inclusion-exclusion. According to the survey data, there are 55 people who like vanilla, 50 who like chocolate, and 5 who do not like either. The total number of people surveyed is 100.

By adding the number of people who like vanilla and chocolate, we get a sum of 105 (55 + 50). This number is greater than the total number surveyed because those who like both flavors are counted twice. To correct this, we must subtract the number of people who don't like either flavor. So, the calculation will be:

Total liking either Vanilla or Chocolate or both = Total liking Vanilla + Total liking Chocolate - Total not liking either

100 = 55 + 50 - Number of people who like both

So:

100 = 105 - Number of people who like both

Number of people who like both = 105 - 100

Number of people who like both = 5

Thus, 5 people liked both vanilla and chocolate ice cream.