Calculating the Percentage of Passing Students in English and Science Exams
This article will guide you through the process of calculating the percentage of students who pass exams in two subjects, English and Science. We'll use a given set of data and some basic principles of probability to find the solution. Let's start by breaking down the problem into manageable parts.
Given Data
The problem states that 30 students give an exam in English, and 25 students give an exam in Science. Moreover, 20 students fail in each subject without additional information on how many students are taking both.
Step-by-Step Calculation
Step 1: Determine the Number of Students Failing in Each Subject
We know that:
20 students fail in English out of 30 who took the exam. 20 students fail in Science out of 25 who took the exam.The calculation for the percentage of students failing each subject is as follows:
Percentage of Students Failing in English
Percentage (Number of failing students / Total students taking the exam) * 100
Percentage of students failing in English (20 / 30) * 100 66.67%
Therefore, 66.67 students fail in English, which is approximately 20 students if we round off to the nearest whole number.
Percentage of Students Failing in Science
Percentage (Number of failing students / Total students taking the exam) * 100
Percentage of students failing in Science (20 / 25) * 100 80%
Therefore, 80 students fail in Science, which is approximately 20 students if we round off to the nearest whole number.
Step 2: Calculate the Number of Students Passing in Each Subject
The total number of students who passed in each subject can be calculated as:
Total passing in English 30 (total students taking English) - 20 (failing students) 10 students
Total passing in Science 25 (total students taking Science) - 20 (failing students) 5 students
Step 3: Use the Principle of Inclusion-Exclusion for Overlapping Classes
Since the data does not specify how many students took both exams, we will assume the worst-case and best-case scenarios. However, the most straightforward calculation under the assumption of independence gives:
Total percentage of students passing at least one subject (using inclusion-exclusion principle)
PPass PPass English PPass Science - PPass both
Without knowing the overlap, the most straightforward calculation under the assumption of independence gives:
PPass at least one 10 (passing English) 5 (passing Science) - 0 (overlap) 15
Thus, the total percentage of students passing at least one subject is 15%.
Conclusion
Using the given data and assumptions, we calculated that the percentage of students passing at least one of the two subjects is 44%. This conclusion is based on the assumption that students who failed one subject also failed the other, and no overlap between the two subjects is considered.
Visualization with Venn Diagram
A Venn diagram can help visualize the overlap between students taking both subjects and those who failed:
In the diagram:
The total number of students taking English is 30. The total number of students taking Science is 25. 20 students failed in each subject, which suggests a possible overlap. Without specific overlap data, we assume no overlap for simplicity.Conclusion
In summary, the percentage of students passing at least one of the exams, assuming no overlap, is 44%. This example demonstrates how to approach and solve such problems with given data and assumptions.