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
It would help if you proofread your questions before you posted them.
What is "85 pass subjects"? What is the missing word?
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To calculate the number of students who pass in different scenarios, we can use set theory and the principle of inclusion-exclusion.
Let's label the sets as follows:
A: Students who passed math
B: Students who passed chemistry
C: Students who passed either math or chemistry
Given the values:
n(A) = 147 (number of students who passed math)
n(B) = 150 (number of students who passed chemistry)
n(C) = 85 (number of students who passed at least one subject)
Now, we can use the principle of inclusion-exclusion to calculate the number of students who pass in different scenarios:
i) Pass math only:
This will be the number of students in set A but not in set B. We can calculate this using the formula:
n(A\B) = n(A) - n(A∩B)
ii) Pass chemistry only:
This will be the number of students in set B but not in set A. We can calculate this using the formula:
n(B\A) = n(B) - n(A∩B)
iii) Passed neither:
This will be the number of students who didn't pass math and didn't pass chemistry. We can calculate this using the formula:
n(A'∩B') = Total students - n(A∪B)
iv) Pass only one subject:
This will be the number of students who passed math only or chemistry only. We can calculate this using the formula:
n(A\B) + n(B\A)
Now, let's calculate the values:
Total number of students = 250
i) Pass math only:
n(A\B) = n(A) - n(A∩B) = 147 - n(A∩B)
ii) Pass chemistry only:
n(B\A) = n(B) - n(A∩B) = 150 - n(A∩B)
iii) Passed neither:
n(A'∩B') = Total students - n(A∪B) = 250 - n(C)
iv) Pass only one subject:
n(A\B) + n(B\A) = 147 - n(A∩B) + 150 - n(A∩B)
Please provide the value of n(A∩B) to calculate these values.
To calculate the number of students who pass:
i) Pass math only:
To find the number of students who pass 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. Since 147 students passed math, and 85 students passed both math and chemistry, the number of students who passed math only is:
147 - 85 = 62
Therefore, 62 students passed math only.
ii) Pass chemistry only:
To find the number of students who pass 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. Since 150 students passed chemistry, and 85 students passed both math and chemistry, the number of students who passed chemistry only is:
150 - 85 = 65
Therefore, 65 students passed chemistry only.
iii) Passed neither:
To find the number of students who passed neither math nor chemistry, we need to subtract the number of students who passed at least one subject from the total number of candidates. Since 85 students passed both math and chemistry, the number of students who passed neither is:
250 - 85 = 165
Therefore, 165 students neither passed math nor chemistry.
iv) Pass only one subject:
To find the number of students who passed only one subject, we can add the number of students who passed math only and the number of students who passed chemistry only:
62 + 65 = 127
Therefore, 127 students passed only one subject.
To summarize:
i) Pass math only: 62 students
ii) Pass chemistry only: 65 students
iii) Passed neither: 165 students
iv) Pass only one subject: 127 students