Question 1177472: . 50 people were surveyed about whether they like the ice cream flavors vanilla and strawberry. 20 people liked vanilla, 25 people liked strawberry, and 30 people liked vanilla or strawberry.
1. How many people like vanilla and strawberry?
2. How many people like exactly one of these two flavors?
3. How many people liked strawberry or did not like vanilla?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. People who like vanilla and strawberry**
We can use the principle of inclusion-exclusion to find the number of people who like both vanilla and strawberry:
* Total who like vanilla or strawberry = Total who like vanilla + Total who like strawberry - Total who like both
Plugging in the given values:
* 30 = 20 + 25 - Total who like both
Solving for the number who like both:
* Total who like both = 20 + 25 - 30 = 15
**Therefore, 15 people like both vanilla and strawberry.**
**2. People who like exactly one flavor**
* People who like only vanilla: 20 (total who like vanilla) - 15 (who like both) = 5
* People who like only strawberry: 25 (total who like strawberry) - 15 (who like both) = 10
So, 5 + 10 = **15 people like exactly one of the two flavors.**
**3. People who liked strawberry or did not like vanilla**
* People who did not like vanilla: 50 (total people) - 20 (who like vanilla) = 30
* People who liked strawberry only: 10 (from previous calculation)
Since we want those who liked strawberry *or* did not like vanilla, we need to be careful not to count those who like both twice. So, we use the principle of inclusion-exclusion again:
* Total who liked strawberry or did not like vanilla = Total who liked strawberry + Total who did not like vanilla - Total who liked strawberry and did not like vanilla
The last group is the same as those who liked strawberry only. Therefore:
* Total who liked strawberry or did not like vanilla = 25 + 30 - 10 = 45
**Therefore, 45 people liked strawberry or did not like vanilla.**
|
|
|
