Question

Examination, 152 Candidates offered Agriculture

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the given details

$n(G)=136,n(P)=128,n(A)=152,n(A\cap G)=52,n(A\cap P)=60,n(A\cap P\cap G)=30,n(P\cap G)=58$

STEP 2: Get the number of students that takes the subjects only

From the basic stuff, we have Number of candidates who had taken only each of the subjects

$\begin{gathered} n(A\text{ only)=}n(A)-\lbrack n(A\cap P)+n(A\cap G)-n(A\cap P\cap G)_{}\rbrack \\ \Rightarrow152-\lbrack52+60-30\rbrack=152-82=70 \\ \\ n(G\text{ only)=}n(G)-\lbrack n(A\cap G)+n(P\cap G)-n(A\cap P\cap G)\rbrack \\ \Rightarrow136-\lbrack52+58-30\rbrack=56 \\ \\ n(P\text{ only)=}128-\lbrack58+60-30\rbrack=40 \end{gathered}$

STEP 3: Represent the values above on a Venn Diagram after getting the values

STEP 4: Find the total number of candidate that sat for the exam.

$\begin{gathered} We\text{ su}m\text{ all the numbers in the Venn diagram to get the total number of candidates that sat for the exam} \\ We\text{ have:} \\ 70+22+30+30+28+56+40=276 \end{gathered}$

Hence, the total number of candidates that sat for the exam is 276

Answer 2

276 number of Candidate that Sat for the exam.

What is Venn Diagram?

Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

Given,

n(G)= Government=136

n(P)=128=Physics

n(A)=152=Agriculture

n(A∩G)=52

n(A∩P)=60

n(G∩P)=58

n(A∩P∩G)=30

n(A only)=n(A)-[n(A∩P)+n(A∩G)-n(A∩P∩G)]

=152-[60+52-30]

=152-82

=70

n(G only)=n(G)-[n(G∩P)+n(A∩G)-n(A∩P∩G)]

=136-[58+52-30]

=56

n(P only)=n(P)-[n(G∩P)+n(A∩P)-n(A∩P∩G)]

=128-[58+60-30]=40

The total number of candidates are

70+22+56+28+40+30+30

=276

Hence 276 number of Candidate that Sat for the exam.

To learn more on Venn diagram click:

brainly.com/question/1605100

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