Represent the following situation using Venn diagrams and answer the questions that follow. In a survey of 100 students in the institute language studies at oxford university, the number of students studying various languages in last four years were found to be : Italian 28, German 30,French 42,Italian and French 10, Italian and German 8, German and French 5, all the three languages 3. (1 point each) a. Venn diagram. b. How many students are studying none of the languages? c. How many students had French as their only language? d. How many students are studying at least one of the languages?

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yeabmelaku56 yeabmelaku56

20-07-2022
Mathematics

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Represent the following situation using Venn diagrams and answer the questions that follow. In a survey of 100 students in the institute language studies at oxford university, the number of students studying various languages in last four years were found to be : Italian 28, German 30,French 42,Italian and French 10, Italian and German 8, German and French 5, all the three languages 3. (1 point each) a. Venn diagram. b. How many students are studying none of the languages? c. How many students had French as their only language? d. How many students are studying at least one of the languages?

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MrRoyal MrRoyal · Answer 1 · 2022-07-24T19:20:46+02:00

There are 80 students studying at least one language

The Venn Diagram

The given parameters are:

Italian = 28
German = 30
French = 42
Italian and French = 10
Italian and German = 8
German and French = 5
Three languages = 3

Using the above parameters, we have:

German and French only = 5 - 3 = 2

Italian and French only = 10 - 3 = 7

Italian and German only = 8 - 3 = 5

French only = 42 - 7 - 2 - 3 = 30

German only = 30 - 2 - 5 - 3 = 20

Italian only = 28 - 7 - 5 - 3 = 13

See attachment for the Venn diagram

Students studying none of the languages

This is calculated as:

None + At least one = Total

Using the Venn diagram, we have:

None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100

This gives

None + 80 = 100

Subtract 80 from both sides

None = 20

Hence, there are 20 students studying none of the languages

Students studying French only

This is calculated as

French only = French - French and Italian - French and German + All three

So, we have:

French only = 42 - 10 - 5 + 3

Evaluate

French only = 30

Hence, there are 30 students studying French only

Students studying at least one

In (b), we have:

None + At least one = Total ⇒ None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100

By comparing both equations, we have

At least one = 3 + 2 + 5 + 7 + 13 + 20 + 30

This gives

At least one = 80

Hence, there are 80 students studying at least one language