Question

A group of 200 people are chosen randomly at a conference. Later, it was found that 120 of them like blue pens and 140 like green pens while 70 like both green and blue pens. Determine the number of people thus chosen who do not like neither green nor blue pens?

• A. 50
• B. 20
• C. 30
• D. 10
• E. 40

Hint:

Use the formula \(n(A \cup B) = n(A) + n(B) - n(A \cap B)\) for such two-set problems.

Answer 1

The Correct Option is D

Step 1: Using Set Theory Formula:
Let \(B\) = set of people who like blue pens, \(G\) = set of people who like green pens.
Given: \(n(B) = 120\), \(n(G) = 140\), \(n(B \cap G) = 70\), Total = 200.

Step 2: Finding People Who Like at Least One:
\[ n(B \cup G) = n(B) + n(G) - n(B \cap G) \]
\[ n(B \cup G) = 120 + 140 - 70 = 190 \]

Step 3: Finding People Who Like Neither:
People who like neither = Total - \(n(B \cup G)\)
\[ = 200 - 190 = 10 \]