In a certain examination 52 candidates offered biology 60 history 96 maths 21 offered both biology and history 22 math and biology 16 math and history if 7 candidates offered all three subject represent the information on a venn diagram how many candidates were there for examination how many candidates offered one subject only how many candidates offered two subject only how many candidates offered at least two subject
impatient much?
give somebody a chance to happen to see what's up.
So - did you actually make a Venn diagram? You have all the numbers.
21-7 = 14 take only biology and history
16-7 = 9 take only math and history
22-7 = 15 take only math and biology
Now you can fill in the numbers for the remaining pieces, which will show how many are taking only a single subject
Then it is trivial to answer the questions.
No
To represent the given information on a Venn diagram, we need to consider three overlapping circles: one each for biology, history, and math.
Let's analyze the information step-by-step:
1. There were 52 candidates who offered biology.
2. There were 60 candidates who offered history.
3. There were 96 candidates who offered math.
4. 21 candidates offered both biology and history.
5. 22 candidates offered both math and biology.
6. 16 candidates offered both math and history.
7. 7 candidates offered all three subjects.
Now, let's place this information on the Venn diagram:
1. Start by drawing three overlapping circles.
2. Label one circle "Biology," another circle "History," and the third circle "Math."
3. In the intersection of all three circles, write the number "7" to represent the candidates who offered all three subjects.
Next, we'll determine the number of candidates for each category you asked about:
1. To find the total number of candidates for the examination, we sum up the number of candidates in each circle.
Total candidates = Candidates in Biology + Candidates in History + Candidates in Math
Total candidates = 52 + 60 + 96
2. To find the number of candidates who offered only one subject, we need to subtract the candidates from the overlapping sections of the circles.
Candidates offered only Biology = Candidates in Biology – (Candidates in Biology and History) – (Candidates in Biology and Math) + Candidates in all three subjects
Candidates offered only History = Candidates in History – (Candidates in Biology and History) – (Candidates in History and Math) + Candidates in all three subjects
Candidates offered only Math = Candidates in Math – (Candidates in Biology and Math) – (Candidates in History and Math) + Candidates in all three subjects
3. To find the number of candidates who offered two subjects only, we need to add up the candidates in the overlapping sections of the circles (excluding candidates in all three subjects).
Candidates offered Biology and History only = Candidates in Biology and History – Candidates in all three subjects
Candidates offered Biology and Math only = Candidates in Biology and Math – Candidates in all three subjects
Candidates offered History and Math only = Candidates in History and Math – Candidates in all three subjects
4. To find the number of candidates who offered at least two subjects, we add the candidates in the overlapping sections of the circles (including candidates in all three subjects).
Candidates offered at least Biology and History = Candidates in Biology and History (including Candidates in all three subjects)
Candidates offered at least Biology and Math = Candidates in Biology and Math (including Candidates in all three subjects)
Candidates offered at least History and Math = Candidates in History and Math (including Candidates in all three subjects)
By following these steps, you can determine the number of candidates in each category and represent the given information on a Venn diagram.