Solution:

Total number of people=125

Let A be the event that people like red colours

\(n(A)=55\)

B be the event that people like blue colours

\(n(B)=60\)

C be the event that people like green colours

\(n(C)=50\)

Let \(A \bigcap B\) be the event that people like both red and blue colors

\(n(A \bigcap B)=25\)

Let \(A \bigcap C\) be the event that people like both red and green colors

\(n(A \bigcap C) =20\)

Let \(B \bigcap C\) be the event that people like both blue and green colors

\(n(B \bigcap C)=30\)

Let \(A \bigcap B \bigcap C\) be the event that people like all three colors

\(n(A \bigcap B \bigcap C)=15\)

To find the probability that the randomly selected person likes only the green colors

P(Green colors)=\(\frac{Number\ of\ people\ like\ green\ colors}{Total\ number\ of\ people}\)

P(Green Colours=\(\frac{50}{125}=0.4\)

P(Green Colors)=0.4

The probability that the randomly selected person likes only the green colors is 0.4