Question

In a survey of 100 students of a school, it is found that 50 study Mathematics, 50 study Physics and 50 study chemistry, 30 study mathematics and Physics, 31 study Mathematics and Chemistry, 32 study Physics and Chemistry and 23 none of these subject. On the study of these give the answer of following question.(i) Number of students who are study all three subject (a) 20 (b) 77 (c) 100 (d) none of these (ii) Which one of the following is correct (a) ∩⊂M. (b) ∩∩⊂M∩ (c) ∪∪100
(iii) If we select a students from survey students what is the probability that the students study all the three subjects (a) 23/100 (b) 1 (c) 1/5 (d) 77/100 (iv) As per survey which subject do most of the students like to study (a) Mathematics (b) Physics (c) Chemistry (d) all three subject (v) How many students study exactly 2 subjects (a) 30 (b) 31 (c) 32 (d) 33
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Answer 1

Given : a survey of 100 students

50 study Mathematics,

50 study Physics

50 study chemistry

30 study Mathematics and Physics

31 study Mathematics and Chemistry,

32 study Physics and Chemistry

23 none of these  subject

To Find :

Number of students who are study all three subject = 20

Solution:

Total = 100

M = 50

P = 50

C =50

M ∩ P = 30

M ∩ C = 31

C ∩ P = 32

None =  23

M ∩ P ∩ C =  All 3 subjects

Total = M + P + C - M ∩ P - M ∩ C - C ∩ P +M ∩ P ∩ C + None

=> 100 = 50 + 50 + 50 - 30- 31 - 32 + M ∩ P ∩ C + 23

=> M ∩ P ∩ C = 20

Number of students who are study all three subject = 20

select a students from survey  students what is the probability that the

students study all the three subjects = 20/100 = 1/5

students study exactly 2 subjects  = M ∩ P+ M ∩ C+ C ∩ P - 3 (M ∩ P ∩ C)

= 30 + 31 + 32 - 3(20)

= 33

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