Question

3. In a class, there are 40 students. 16 students opted for history but not geography and 26 students opted for history. If all the students opted for at least one of the subjects, how many students have opted for geography?​

Answer 1

Answer:

3. In a class, there are 40 students. 16 students opted for history but not geography and 26 students opted for history. If all the students opted for at least one of the subjects, how many students have opted for geography?

Answer 2

Step-by-step explanation:

Number of students opted mathematics =n(M)=30

Number of students opted Biology =n(B)=32

Number of students opted both Mathematics and Biology =n(M∩B)=24

Number of students opted Mathematics or Biology =(M∪B)

n(M∪B)=n(M)+n(B)−n(M∩B)

⇒n(M∪B)=30+32−24=38

(i) Probability that student opted Mathematics or Biology =

n

n(M∪B)

=

60

38

=

30

19

(ii) Probability that student has opted neither mathematics nor Biology =1−P(M∪B)=1−

30

19

=

30

11

Number os students opted only Mathematics =n(M)−n(M∩B)=30−24=8

(iii) Probability of selecting students who opted only mathematics =

60

8

=

15

2