In Samsung UBS, 25 students in class took an examination in mathematics and science. 17 of them passed science and 8 passed in both mathematics and science. 3 students did not pass in any of the subject. Find A. Illustrate the information on a Venn diagram. B. How many passed in mathematics? C. The probability of meeting a student who passed in one subject only
A. To illustrate the information on a Venn diagram, we can use circles to represent mathematics and science, with an overlap indicating the students who passed in both subjects.
First, let's draw two circles to represent mathematics (M) and science (S):
M S
Next, we can fill in the information we know:
- 8 students passed in both subjects, so we fill in the overlap of the circles with the number 8.
- 17 students passed in science, so we fill in the remaining part of the circle representing science with the number 17.
- 3 students did not pass in any subject, so we leave a space outside of both circles and write 3.
The Venn diagram should now look like this:
M S
8
3
17
B. To find how many passed in mathematics, we need to calculate the number of students in the mathematics circle.
Since 8 students passed in both subjects and 17 students passed in science, we can subtract the number of students who passed in both subjects from the total number of students who passed in science.
So, the number of students who passed in mathematics is 17 - 8 = 9.
Therefore, 9 students passed in mathematics.
C. The probability of meeting a student who passed in one subject only can be calculated by dividing the number of students who passed in one subject only by the total number of students.
To find the number of students who passed in one subject only, we need to subtract the number of students who passed in both subjects and the number of students who did not pass any subject from the total number of students.
So, the number of students who passed in one subject only is 25 - 8 - 3 = 14.
The probability of meeting a student who passed in one subject only is 14/25.
Therefore, the probability is 14/25 or 0.56.