Out of 400 students to n the final year in a secondary school,300 are offering biology and 190 are offering chemistry
I.How many students are offering both biology and chemistry,if only 70 students are offering neither biology nor chemistry
ii.how many students are offering at least one of biology or chemistry
Yes
This is ideal for a Venn diagram solution.
In a rectangle representing the universal set of 400 students, draw
two intersecting circles labeled B and C
Label their intersection as x
label the "B only" as 300-x
labe the "C only" as 190-x
label the part outside the circle, but inside the rectangle as 70
300-x + x + 190-x + 70 = 400
i) solve or x
ii) that would clearly be 400-70 = ...
(curious to know where it is common to say "I am offering Biology" instead
of "I am taking Biology" ? )
Answer
To find the number of students offering both biology and chemistry, we need to use the concept of set theory and the principle of inclusion-exclusion.
i. To find the number of students offering both biology and chemistry, we need to subtract the number of students offering neither biology nor chemistry from the total number of students. We can use the formula:
Number of students offering both biology and chemistry = Total number of students - Number of students offering neither biology nor chemistry
In this case, we have:
Total number of students (n) = 400
Number of students offering biology (B) = 300
Number of students offering chemistry (C) = 190
Number of students offering neither biology nor chemistry = 70
Using the principle of inclusion-exclusion, we can calculate the number of students offering both biology and chemistry as follows:
Number of students offering both biology and chemistry = (Number of students offering biology) + (Number of students offering chemistry) - (Number of students offering neither biology nor chemistry)
Number of students offering both biology and chemistry = 300 + 190 - 70
Number of students offering both biology and chemistry = 420
Therefore, there are 420 students offering both biology and chemistry.
ii. To find the number of students offering at least one of biology or chemistry, we need to calculate the union of the number of students offering biology and the number of students offering chemistry.
Number of students offering at least one of biology or chemistry = (Number of students offering biology) + (Number of students offering chemistry) - (Number of students offering both biology and chemistry)
Number of students offering at least one of biology or chemistry = 300 + 190 - 420
Number of students offering at least one of biology or chemistry = 70
Therefore, there are 70 students offering at least one of biology or chemistry.