draw a Venn diagram that represents this question:in an exam, 31 candidate passed chemistry, 29 passed physics and 3 failed both subject.if 50 candidate sat for the exam how many of them passed chemistry
To represent this question in a Venn diagram, we will have two circles. One circle will represent chemistry and the other will represent physics. The overlapping region will represent the students who have passed both chemistry and physics.
Let's label the circles as follows:
- Circle A: Chemistry
- Circle B: Physics
We know that 31 candidates passed chemistry, 29 candidates passed physics, and 3 candidates failed both subjects.
So, the Venn diagram would look like this:
A: Chemistry
_______________
| _ _ _ _ _ _ _ _ _
| | |
| | 3 |
| |_ _ _ _ _| |
| |
| _ _ _ _ _ _ _ _ _
| | |
| | 31 |
| |_ _ _ _ _| |
|
B: Physics
To find out how many students passed chemistry, we can add the number of students in circle A (chemistry) and the number of students in the overlapping region.
So, the number of students who passed chemistry is 31 + 3 = 34.
To represent the given information in a Venn diagram, we can use the following steps:
Step 1: Draw two overlapping circles to represent the subjects Chemistry and Physics.
Step 2: Label the circles with the names of the subjects (Chemistry and Physics).
Step 3: Write the number of candidates who passed Chemistry (31) outside the circle representing Chemistry.
Step 4: Write the number of candidates who passed Physics (29) outside the circle representing Physics.
Step 5: Write the number of candidates who failed both subjects (3) in the overlapping region of the two circles.
Step 6: Calculate the number of candidates who passed both Chemistry and Physics by subtracting the number of candidates who failed both (3) from the number who passed Chemistry (31). In this case, it would be 31 - 3 = 28.
Step 7: Add the number of candidates who passed Chemistry (31) and the number who passed both subjects (28) to find the total number of candidates who passed Chemistry. In this case, it would be 31 + 28 = 59.
So, the Venn diagram would show that 59 candidates passed Chemistry.
To represent the given information in a Venn diagram, we need to consider three categories: candidates who passed chemistry, candidates who passed physics, and candidates who failed both subjects.
First, we start by drawing two overlapping circles to represent the sets of candidates who passed chemistry (C) and those who passed physics (P). To account for the 3 candidates who failed both subjects, we show an overlapping region in the center of the diagram where the two circles intersect.
To find out how many candidates passed chemistry, we need to consider the candidates within the chemistry circle (C) and those in the overlapping region (representing those who passed both chemistry and physics).
Using the given information:
- 31 candidates passed chemistry (C)
- 29 candidates passed physics (P)
- 3 candidates failed both subjects
We can now construct the Venn diagram:
1. Draw two overlapping circles.
2. Label one circle as "Chemistry" (C) and the other as "Physics" (P).
3. Inside the C circle, write "31" to represent the 31 candidates who passed chemistry.
4. Inside the P circle, write "29" to represent the 29 candidates who passed physics.
5. In the overlapping region of the two circles, write "3" to represent the candidates who failed both subjects.
Now, to find the number of candidates who passed chemistry, we need to add the number of candidates in the C circle and overlapping region: 31 + 3 = 34.
So, 34 candidates passed chemistry out of the total 50 candidates who sat for the exam.