of 250 candidates writing a exam, 147 passed in math,150 pass in chemistry and 85 pass subjects
B)calculate the number of students who pass
i)pass math only
ii)pass chemistry only
iii)passed neither
iv)pass only one subject
Let's use a Venn diagram to help us solve this problem.
Let M be the set of students who passed math.
Let C be the set of students who passed chemistry.
Let T be the total number of students (250 in this case).
We are given the following:
| M ∪ C | = T (the total number of students)
| M | = 147 (students passed in math)
| C | = 150 (students passed in chemistry)
|M ∩ C | = 85 (students pass both subjects)
Now, let's calculate the following:
i) | M - C | (students passed only in math)
To find the number of students who passed only in math, we need to subtract the number of students who passed in both math and chemistry: | M - C | = | M | - | M ∩ C | = 147 - 85 = 62 students.
ii) | C - M | (students passed only in chemistry)
To find the number of students who passed only in chemistry, we need to subtract the number of students who passed in both math and chemistry: | C - M | = | C | - | M ∩ C | = 150 - 85 = 65 students.
iii) (students who passed neither)
To find the number of students who passed neither math nor chemistry, we can use the formula for the total number of students:
| M ∪ C | = | M - C | + | M ∩ C | + | C - M | + |neither|
Now we can substitute our known values into the equation and solve for the number of students who passed neither:
250 = 62 + 85 + 65 + |neither|
250 = 212 + |neither|
|neither| = 250 - 212 = 38 students
iv) (students who passed only one subject)
To find the number of students who passed only one subject, we can simply add the number of students who passed only in math and those who passed only in chemistry: 62 + 65 = 127 students.
In summary, the number of students who
i) passed math only: 62
ii) passed chemistry only: 65
iii) passed neither: 38
iv) passed only one subject: 127
To calculate the number of students who pass:
First, we add the number of students who passed in math and chemistry: 147 + 150 = 297.
i) To find the number of students who passed math only, we subtract the number of students who passed both math and chemistry from the total number of students who passed in math: 147 - 85 = 62.
ii) To find the number of students who passed chemistry only, we subtract the number of students who passed both math and chemistry from the total number of students who passed in chemistry: 150 - 85 = 65.
iii) To find the number of students who passed neither subject, we subtract the total number of students who passed (297) from the total number of students who wrote the exam (250): 250 - 297 = -47. However, the number of students who passed neither cannot be negative. Therefore, there might be an error in the given data.
iv) To find the number of students who passed only one subject, we add the number of students who passed math only (62) with the number of students who passed chemistry only (65): 62 + 65 = 127.
Note: Please double-check the data to ensure there are no errors.
To calculate the number of students who passed:
i) Passed math only:
To find the number of students who passed math only, we need to subtract the number of students who passed both math and chemistry from the total number of students who passed math. In this case, 147 students passed math and 85 students passed both math and chemistry. So, the number of students who passed math only would be 147 - 85 = 62.
ii) Passed chemistry only:
Similarly, to find the number of students who passed chemistry only, we need to subtract the number of students who passed both math and chemistry from the total number of students who passed chemistry. In this case, 150 students passed chemistry and 85 students passed both math and chemistry. So, the number of students who passed chemistry only would be 150 - 85 = 65.
iii) Passed neither:
To calculate the number of students who passed neither subject, we need to subtract the number of students who passed either math or chemistry or both from the total number of students. In this case, 250 students wrote the exam, and 85 students passed both math and chemistry. So, the number of students who passed neither would be 250 - 85 = 165.
iv) Passed only one subject:
To calculate the number of students who passed only one subject, we need to subtract the number of students who passed both math and chemistry from the sum of students who passed math only and students who passed chemistry only. In this case, 85 students passed both math and chemistry, 62 students passed math only, and 65 students passed chemistry only. So, the number of students who passed only one subject would be 62 + 65 - 85 = 42.
Therefore, based on the given information:
i) The number of students who passed math only is 62.
ii) The number of students who passed chemistry only is 65.
iii) The number of students who passed neither subject is 165.
iv) The number of students who passed only one subject is 42.