Answer :
Answer:
Let's tackle each part of the problem step-by-step.
Part (a): Venn Diagram
We can use a Venn diagram to illustrate the given information. Let's denote:
A as the set of students who failed Account.
E as the set of students who failed English.
A∩E as the set of students who failed both subjects.
Given:
50% of students failed Account (∣A∣=50%)
30% of students failed English (∣E∣=30%)
25% of students failed both subjects (∣A∩E∣=25%)
We can represent this information in a Venn diagram.
Part (b): Percentage of Candidates Who Passed Both Subjects
To find the percentage of students who passed both subjects, we need to find the percentage of students who did not fail either subject.
Using the principle of inclusion and exclusion for sets:
\[ |A \cup E| = |A| + |E| - |A \cap E| \]
\[ |A \cup E| = 50\% + 30\% - 25\% = 55\% \]
So, 55% of students failed at least one subject. Therefore, the percentage of students who passed both subjects is:
\[ 100\% - 55\% = 45\% \]
Part (c): Number of Students Who Passed Both Subjects
We know that 25% of students failed both subjects, and this corresponds to 225 students. Let's use this information to find the total number of students.
Let N be the total number of students. Then:
\[ 0.25N = 225 \]
\[ N = \frac{225}{0.25} = 900 \]
Now, we need to find the number of students who passed both subjects. We know that 45% of students passed both subjects:
\[ 0.45N = 0.45 \times 900 = 405 \]
Answer:
b) 45%
c)405 students
Step-by-step explanation:
a) Venn Diagram
Venn diagrams are diagrams that uses circles representing certain elements that are overlapping to each other to show a relation between those elements. In this case, the two elements are the students who failed Account and the students who failed English. The element that overlaps both of them is students who failed both subjects.
Therefore, the diagram should look something like this (below).
b) Percentage of the candidates who passed both subjects
The first instinct one would have is to just subtract 100 from the percentage of those who failed both subjects, but that is not the case since 75% of those who didn't fail both subjects, still might've failed one of them. Therefore, you have to look at the all the given values as a whole.
First of all, you have to take into account that the 25% of those who failed both subjects are part of the 30% and 50% who failed one of the subjects. So if we subtract 25 from 50, that means 25% of students only failed Account. If we subtract 25 from 30, that means 5% have only failed English.
Now we have the important informations, 25% failed only Account, 5% only English, and 25% both. If we add all of them up 25+5+25 = 55%. That means 55% have failed at least something. So by subtracting 55 from 100, we know that 45% have passed both of subjects.
c) how many students passed both?
Now using the percentage of students who failed both, we know that 25% is 25/100. The 100 represents the complete number of subjects in a set. So if 225 students failed, that means 225 is 25% of the class. To know how many students are in the classroom, just cross multiply and divide. (100*225)/25 = 900 students total.
Based on the previous calculation that helped us find the percentage of students who passed both subjects, just multiply the total number of students by the percentage, (45/100)*900 = 405 students.
