In a group of 100 persons 72 people can speak english and 43 can speak french. How many can speak English only ? How many can speak french only and how many can speak english and french?
Answers
ans-two group speak in English=100 and 72
since, 100+72=172 speak English only
In other hand ,there are 43 people who speak France only.clearly. so 43 people speaks only France.
So, 172 speaks English and 43 speaks French.
Given:
Number of people who speak English n(A) = 72 People
Number of people who speak French n(B) = 43 People
Total number of people in the group = 100 People
Calculating the number of people that can speak both French and English:
n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
Substituting all the values known to us in this formula we get:
= 72 + 43 - 100
= 115 - 100
= 15
Therefore, 15 people can speak both French and English.
Calculating the number of people who speak English only:
n(A) = n(A - B) + n(A ∩ B)
Substituting all the values known to us in this formula we get:
= 72 - 15
= 57
Therefore, 57 people can speak only English.
Calculating the number of people who speak only French:
n(B - A) = n(B) - n(A ∩ B)
Substituting all the values known to us in this formula we get:
= 43 - 15
= 28
Therefore, 28 people can only speak French.