100 students were interviewed. 28 took Physical Education, 31 took Biology, 42 to English, 9 took Physical Education and Biology, 10 took Physical Education and English and 6 took Biology and English.
i. How many students took none of the three subjects [4]
ii. How many took Physical Education ,but not Biology or English [4]
iii. How many student took Biology and Physical Education but not English [4]
Answers
Answer:
i. How many students took none of the three subjects? = 20
ii. How many took Physical Education ,but not Biology or English? = 13
iii. How many student took Biology and Physical Education but not English? = 5
Step-by-step explanation:
According to the information given in the question above, a figure is drawn below for reference, and further the calculations are done as follows:
Step 1:
We are given that,
No. of students who took both Physical education & Biology = 9
No. of students who took both Physical education & English = 10
No. of students who took both Biology & English = 6
Since we are not given any information about the students taking all the three subjects so one of the ways that it can be calculated from the Venn diagram of the figure is as follows : (5+4 = 9) or (6+4=10) or (2+4= 6).
∴ No. of students who took all the 3 subjects = 4
Step 2:
Here we are given,
Total no. of students who took Physical education = 28
Total no. of students who took Biology = 31
Total no. of students who took English = 42
Therefore,
No. of students taking only Physical education (not Bio & Eng) = 28 – (5+6+4) = 13
No. of students taking only Biology (not P.E. & English)= 31 – (5+4+2) = 20
No. of students taking only English (not P.E. & Bio) = 42 – (6+4+2) = 30
Step 3:
Since,
A total no. of 100 students were interviewed
∴ No. of students who took none of the 3 subjects = 100 – (13+5+4+20+2+30+6) = 20
Step 4:
Now, from the Venn diagram, we can see that,
No. of students who took Biology and Physical Education but not English = 5
Answer:
Step-by-step explanation:
