30 people were surveyed about their favourite type of pet: 15 people liked cats, 20 people liked dogs and 10 people liked both. Determine how many people liked dogs or cats:(I:1)

Question

BlackTom AI · Accepted Answer

We start by identifying the given sets: let A be the group that likes cats and B be the group that likes dogs. The data provides: |A| = 15, |B| = 20, and |A ∩ B| = 10. The quantity asked is the number of people who liked dogs or cats, which is the union |A ∪ B|.

Apply the inclusion–exclusion principle: |A ∪ B| = |A| + |B| − |A ∩ B|. Substituting the numbers: 15 + 20 − 10 = 25.

Now evaluate each answer choice:
- Option a: 10. This is exactly |A ∩ B|, the number who like both cats and dogs, not the total who like either. It ignores those who like only cats or only dogs, so it’s too small.
- Option b: 30. If you summed |A| and |B| without subtracting the overlap, you’d get 35, but a double-counted intersection must be removed. 30 reflects some misaccounting, but it’s not the correct union value given the overlap of 10.
- Option c: 35. This is the sum |A| + |B|, which double-counts those who like both pets. It does not adjust for the overlap, so it overestimates the union.
- Option d: 25. This matches the inclusion–exclusion calculation |A ∪ B| = 15 + 20 − 10 = 25, correctly accounting for the overlap of 10 people who like both.

Thus, by properly combining the counts and removing the overlap, the correct total of people who liked dogs or cats is 25.

30 people were surveyed about their favourite type of pet: 15 people liked cats, 20 people liked dogs and 10 people liked both. Determine how many people liked dogs or cats:(I:1)

查看解析

登录即可查看完整答案

类似问题

Sample Numeric Answer Question There are 12 people in a room. Six people are wearing socks and four people are wearing shoes; three people are wearing both. How many are in bare feets?

Sample Numeric Answer Question There are 12 people in a room. Six people are wearing socks and four people are wearing shoes; three people are wearing both. How many are in bare feet?

In a group of 50 students: - 20 like hiking - 25 like biking - 10 like both How many like either hiking or biking?

If a class of 40 students includes 18 who play basketball and 15 who play football, with 7 playing both, how many students play at least one of the sports?

In a survey of 500 people:55% use Instagram 45% use Reddit 35% use TikTok 25% use both Instagram and Reddit 15% use both Instagram and TikTok 10% use both Reddit and TikTok 5% use all three What percentage of people use at least one of the three apps?

In set theory, which is the correct formula for the Principal of Inclusion and Exclusion: (K:1)

30 people were surveyed about their favourite type of pet: 15 people liked cats, 20 people liked dogs and 10 people liked both. Determine how many people liked dogs or cats:(I:1)

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单