in a school, 37% of the pupils study principle of accounts and 28% study principal of business. if 15% study both business subjects what percentage of the pupils do not study neither, study P.O.B only and study P.O.A only
To find the percentages of pupils who do not study either subject, study P.O.B only, and study P.O.A only, we need to use the concept of set theory and the formula for finding the percentage of a subset when the percentages of the whole set and the overlapping subset are known.
Let's assume there are 100 pupils in the school.
Given:
- 37% study Principle of Accounts (P.O.A)
- 28% study Principle of Business (P.O.B)
- 15% study both P.O.A and P.O.B
To find the percentage of pupils who do not study either subject, we need to subtract the students studying P.O.A and/or P.O.B from the total number of pupils (100%).
Step 1: Find the percentage of pupils who study either P.O.A or P.O.B.
To find this percentage, we sum up the percentages of students studying each subject individually and subtract the percentage of students studying both subjects.
P(O.A or O.B) = P(O.A) + P(O.B) - P(O.A and O.B)
P(O.A or O.B) = 37% + 28% - 15%
P(O.A or O.B) = 50%
Step 2: Find the percentage of pupils who do not study either P.O.A or P.O.B.
To find this percentage, we subtract the percentage of students studying either P.O.A or P.O.B from 100%.
P(neither P.O.A nor P.O.B) = 100% - P(O.A or O.B)
P(neither P.O.A nor P.O.B) = 100% - 50%
P(neither P.O.A nor P.O.B) = 50%
Step 3: Find the percentage of pupils who study P.O.A only.
To find this percentage, we subtract the percentage of students studying both subjects from the percentage of students studying P.O.A.
P(P.O.A only) = P(O.A) - P(O.A and O.B)
P(P.O.A only) = 37% - 15%
P(P.O.A only) = 22%
Step 4: Find the percentage of pupils who study P.O.B only.
To find this percentage, we subtract the percentage of students studying both subjects from the percentage of students studying P.O.B.
P(P.O.B only) = P(O.B) - P(O.A and O.B)
P(P.O.B only) = 28% - 15%
P(P.O.B only) = 13%
Therefore, the percentages are:
- Students who do not study either P.O.A nor P.O.B: 50%
- Students who study P.O.A only: 22%
- Students who study P.O.B only: 13%