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) 9 ∩ ; ⊂ M.
(b) 9 ∩ > ∩ ; ⊂ M ∩ >
(c) 9 ∪ > ∪ ; 6 100
i) 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
) 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
Answers
Answer:
please.... anyone answer these questions
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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