Question:
In a committee, 50 people speak Hindi, 20 speak English and 10 speak both Hindi and English. How many speak at least one of these two languages?
Solution:
Given:
People who speak Hindi = 50
People who speak English = 20
People who speak both English and Hindi = 10
To Find: People who speak at least one of these two languages
Let us consider,
People who speak Hindi = n(H) = 50
People who speak English = n(E) = 20
People who speak both Hindi and English $=n(H \cap E)=10$
People who speak at least one of the two languages $=n(H \cup E)$
Venn diagram:
Now, we know that,
$n(A \cup B)=n(A)+n(B)-n(A \cap B)$
Therefore,
$n(H \cup E)=n(H)+n(E)-n(H \cap E)$
$=50+20-10$
$=60$
Thus, People who speak at least one of the two languages are 60.