Answer:
Option 3 - 51%
Step-by-step explanation:
Given : In a class of 160 students, 90 are taking math, 78 are taking science, and 62 are taking both math and science.
To find : What is the probability of randomly choosing a student who is not taking science?
Solution :
We can show this situation through Venn diagram,
Refer the attached figure below.
Take the Blue circle as the students taking math and Red circle as the student taking science.
Total number of student = 160
Let M be the student taking math M=90
S be the student taking math S=78
\(M\cap S=B=62\)
The student only take math is 90-62=28=P
The student only take science is 78-62=16=Q
Total students cover the circle is 28+62+16 = 106
Remaining students who are not in either two circles is 160-106=54
The remaining students and student taking math only is 28+54=82
So, 82 students are those who are not taking science.
The probability of student who is not taking science is
\(P=\frac{82}{160}=\frac{41}{80}=0.51\)
In percentage, 0.51=51%.
Therefore, Option 3 is correct.
The probability of student who is not taking science is 51%.
