A Venn diagram shows the number of pupils who passed in Maths, English, and General paper. Calculate the number of pupils for the following:

Here are the solutions for question 3 based on the provided Venn diagram:

• M = {pupils who passed in Maths}
• E = {pupils who passed in English}
• G = {pupils who passed in General paper}

From the Venn diagram:

• Pupils who passed in Maths only: 3
• Pupils who passed in English only: 11
• Pupils who passed in General paper only: 8
• Pupils who passed in Maths and English only: 4
• Pupils who passed in Maths and General paper only: 20
• Pupils who passed in English and General paper only: 6
• Pupils who passed in Maths, English, and General paper: 10
• Pupils who failed in all subjects (outside all circles): 18

a) How many pupils passed in English only?
This is the number in the 'E' circle that does not overlap with 'M' or 'G'.

$$\text{Pupils passed in English only} = 11$$

• 11 pupils

b) How many pupils passed in General paper?
This is the total number of pupils within the 'G' circle.

$$\text{Pupils passed in General paper} = (\text{G only}) + (\text{M and G only}) + (\text{E and G only}) + (\text{M, E, and G})$$ $$= 8 + 20 + 6 + 10 = 44$$

• 44 pupils

c) How many pupils passed in all the subjects?
This is the number of pupils in the intersection of all three circles (M, E, and G).

$$\text{Pupils passed in all subjects} = 10$$

• 10 pupils

d) How many pupils failed in all the subjects?
This is the number of pupils outside all three circles.

$$\text{Pupils failed in all subjects} = 18$$

• 18 pupils

e) How many pupils passed in Maths and General paper?
This is the total number of pupils in the intersection of 'M' and 'G'. This includes those who passed in Maths and General paper only, and those who passed in Maths, English, and General paper.

$$\text{Pupils passed in Maths and General paper} = (\text{M and G only}) + (\text{M, E, and G})$$ $$= 20 + 10 = 30$$

• 30 pupils

f) In which subjects did the pupils pass most?
To determine this, we need to calculate the total number of pupils who passed in each subject.

Total passed in Maths (M):

$$3 + 4 + 20 + 10 = 37$$

Total passed in English (E):

$$11 + 4 + 6 + 10 = 31$$

Total passed in General paper (G):

$$8 + 20 + 6 + 10 = 44$$

Comparing the totals: Maths (37), English (31), General paper (44). The highest number is 44, which corresponds to General paper.

• General paper