In a committee, 50 people speak Hindi, 20 speak English and 10 speak

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.