50 in a class took an examination in french and mathematics . 14 of them pass french only , 23 pass in both subjects and 5 of them failed in both subjects. Find
1. The number of students who passed in french.
2. The number of students who passed in only one subject
To solve this problem, we can use a Venn diagram.
Let's label the different regions of the Venn diagram as follows:
- The region representing students who passed in French only is labeled "F"
- The region representing students who passed in both French and Mathematics is labeled "F∩M"
- The region representing students who passed in Mathematics only is labeled "M"
- The region representing students who failed in both subjects is labeled "Neither"
From the given information, we can start filling in the Venn diagram:
- 14 students pass French only, so we write 14 in region F.
- 23 students pass in both subjects, so we write 23 in region F∩M.
- 5 students failed in both subjects, so we write 5 in region Neither.
Now, we can find the number of students who passed in French by adding up the number of students in regions F and F∩M:
14 + 23 = 37. Therefore, 37 students passed in French (including those who passed in both subjects).
To find the number of students who passed in only one subject, we need to subtract the number of students who passed in both subjects (region F∩M) from the total number of students who passed in either subject (region F + region M):
37 - 23 = 14. Therefore, 14 students passed in only one subject.