In an examination of certain number of candidates 18 passed mathematics, 17 passed physics, 11 passed both mathematics and physics, 1 failed both subjects. Find the number of candidates that passed. i. Mathematics only. ii. Physics only. iii. Total number of candidates that sat for the examination. iv. Show in on venn diagram.
the number who passed something is
18+17-11 = 24
Now just draw the usual Venn diagram to answer the questions.
What are the numbers of candidates that failed only mathematics
To solve this problem, we can use the principle of inclusion-exclusion. Let's break down the information given:
Total number of candidates who passed mathematics = 18.
Total number of candidates who passed physics = 17.
Number of candidates who passed both mathematics and physics = 11.
Number of candidates who failed both subjects = 1.
To find the number of candidates who passed mathematics only, we need to subtract the candidates who passed both subjects from the total number of candidates who passed mathematics:
Candidates passed mathematics only = Total candidates passed mathematics - Candidates passed both subjects
Candidates passed mathematics only = 18 - 11
Candidates passed mathematics only = 7
So, there are 7 candidates who passed mathematics only.
To find the number of candidates who passed physics only, we can follow a similar approach:
Candidates passed physics only = Total candidates passed physics - Candidates passed both subjects
Candidates passed physics only = 17 - 11
Candidates passed physics only = 6
So, there are 6 candidates who passed physics only.
To find the total number of candidates who sat for the examination, we can add the candidates who passed mathematics only, the candidates who passed physics only, the candidates who passed both subjects, and the candidates who failed both subjects:
Total candidates = Candidates passed mathematics only + Candidates passed physics only + Candidates passed both subjects + Candidates failed both subjects
Total candidates = 7 + 6 + 11 + 1
Total candidates = 25
So, there were 25 candidates who sat for the examination.
To represent this information on a Venn diagram, we can draw three overlapping circles: one for mathematics, one for physics, and one for the intersection of mathematics and physics. The numbers are as follows:
Mathematics only = 7
Physics only = 6
Both mathematics and physics = 11
Failed both subjects = 1
The remaining candidates who neither passed mathematics nor physics (i.e., neither in mathematics only nor in physics only nor in both) will be outside all the circles.
I hope this helps! Let me know if you have any further questions.