Answer following questions mathematic.
There are 50 student in a classroom who took an examination in french and mathematic
If 14 of them pass french only 23 passed in both french and mathematic and 5 them failed in both subject
I. Illustrate the information on a venn diagram.
II. Pass french and mathematic only (9)
III. Pass exactly one subject (14 )
To create a Venn diagram for the given situation, we'll need two circles that overlap. One circle represents students who passed in French, the other circle represents students who passed in Mathematics.
I. Here's how you might draw the Venn diagram based on the information provided:
- Draw two circles that overlap. Label one circle "French" and the other "Mathematics".
- In the overlapping area (which represents students passing both subjects), write the number 23 because 23 students passed in both French and Mathematics.
- Since 14 students passed only French, we will place the number 14 in the part of the French circle that does not overlap with the Mathematics circle.
- We have 5 students that failed both subjects. The number of students that took the exam is 50. Therefore, the total number of students that passed at least one subject will be 50 - 5 = 45.
- We need to find out how many passed only Mathematics. To get this number, we subtract the number of students who passed both from the total who passed at least one subject: 45 (students passing one or both) - 23 (students passing both) - 14 (students passing only French) = 8 students who passed only Mathematics.
Using these pieces of information, we can now flesh out our Venn diagram as follows:
```
French
-------------
| |23 | |
| 14 |----| 8 |
|_____| |____|
Mathematics
```
II. The statement "Pass french and mathematic only (9)" contradicts the information given, as 23 students passed both subjects, not 9. So this is either additional information that wasn't reflected in the initial data, or it is an error.
III. To find the number who passed exactly one subject (either French or Mathematics but not both), we add the number who passed only French to the number who passed only Mathematics.
Passed only French: 14
Passed only Mathematics: 8
Passed exactly one subject: 14 + 8 = 22
Again, the statement "Pass exactly one subject (14)" appears to be an error, since the calculated number indicates that 22 students passed exactly one subject, not 14.
If we consider 9 students passed only French and Mathematic, instead of 23 passing both, then the Venn diagram would need adjustment:
- The overlap has the number 9 for those passing both subjects.
- Since we want 14 students to pass exactly one subject, and considering the 9 who passed both, we would deduct 9 from the 14, leaving us with 5 students who passed only one subject.
- We already know there are 5 students who failed both subjects. Therefore, students who passed only one of the subjects or both would then be 50 - 5 (those who failed both) = 45 students.
- Adjusting for the overlap, we would have 45 - 9 (both subjects) = 36 students passing at least one subject.
- We then split this into 14 for French only (as given) and determine the number for Mathematics only by subtracting the 14 from the remaining count: 36 - 14 = 22 for Mathematics only.
But note, this revised illustration doesn't align with the initial data given (22 students passing only Mathematics is not consistent with the 14 given as passing exactly one subject). It's important to clarify the exact parameters of the problem before proceeding in such cases.