Suppose there are 70 students in an examination with the students writing at least one of the subjects; Chemistry, Physics and Biology. Thirty(30) students offer Physics, 33 offer Chemistry and 40 offer biology, 10 students offer both Physics and Chemistry. Fourteen (14) of the students offer Physics and Biology, and 15 of them offer Biology and Chemistry. How many students offer only Biology
are you familiar with Venn Diagrams? ... three intersecting circles?
Just to get you started, if x offer all three subjects, you have
(33+30+40)-(10+14+15)+x = 70
To find out the number of students who offer only Biology, we need to use the principle of inclusion-exclusion.
First, let's identify the number of students who offer multiple subjects:
- The number of students who offer Physics and Chemistry is given as 10.
- The number of students who offer Physics and Biology is given as 14.
- The number of students who offer Biology and Chemistry is given as 15.
Now, let's calculate the total number of students who offer multiple subjects:
- Students who offer Physics and Chemistry: 10
- Students who offer Physics and Biology: 14
- Students who offer Biology and Chemistry: 15
To find out the total number of students who offer multiple subjects, we add these three numbers: 10 + 14 + 15 = 39.
Now, let's calculate the number of students who offer only one subject:
- Students who offer Physics only: 30 - (10 + 14) = 6
- Students who offer Chemistry only: 33 - (10 + 15) = 8
Finally, to find out the number of students who offer only Biology, we subtract the number of students who offer multiple subjects and the number of students who offer Biology and Chemistry from the total number of students who offer Biology.
Students who offer Biology only = Total number of students who offer Biology - Students who offer Biology and Chemistry - Students who offer Biology and Physics = 40 - 15 - 14 = 11
Therefore, 11 students offer only Biology.