Question

In a survey of 150 music lovers, it was found that 90 people liked folk songs, 70 people liked modern songs, and 30 did not like both the songs. What is the total number of people who liked at least one of the two types of songs?

a) 90
b) 70
c) 30
d) 130

Answer 1

By using the principle of inclusion and exclusion, we find that 130 music lovers out of 150 surveyed liked at least one of the two types of songs, which is the correct answer. Therefore, the correct answer is d) 130.

Step-by-step explanation:

In the survey of 150 music lovers, we can use the principle of inclusion and exclusion to find out how many people liked at least one of the two types of songs: folk and modern. We should first add the number of people who like folk songs to the number of people who like modern songs. However, if we do that directly, we are counting the people who like both twice. This is where we need to use exclusion. Since 30 people do not like both songs, we add the two groups of song likers and then subtract the number who don't like either.

So, the calculation would be: 90 (folk song likers) + 70 (modern song likers) - 30 (people who don't like either) = 130 people who liked at least one of the two types of songs.

Therefore, the correct answer is d) 130.