In a survey of 400 students of a college it was found that 240 study mathematics, 180 study Statistics and 140 study Accounts, 80 study mathematics and Statistics, 60 study Statistics and Accounts, 100 study Accounts and mathematics and 40 study none of these subjects. On the basis of this information answer the following questions.
Find the number of students who study at least one of these subjects.
Find the number of students who study all of these subjects
Answers
(a) The number of students who study at least one of these subjects is 360.
(b) The number of students who study all of these subjects is 40.
Step-by-step explanation:
Let M, S and A represents the following events.
M = Mathematics
S = Statistics
A = Accounts
Number of student = 400
240 study mathematics : n(M) = 240
180 study Statistics : n(S) = 180
140 study Accounts: n(A) = 140
80 study mathematics and Statistics : n(M∩S) = 80
60 study Statistics and Accounts : n(S∩A) = 60
100 study Accounts and mathematics : n(A∩M) = 100
40 study none of these subjects : n(M'∩S'∩A') = 40
(a)
We need to find the number of students who study at least one of these subjects.
Students who study at least one of these subjects = Total students - Number of students who study none of these subjects.
Therefore, the number of students who study at least one of these subjects is 360.
(b)
We need to find the number of students who study all of these subjects.
Substitute the given values.
Subtract both sides by 320.
Therefore, the number of students who study all of these subjects is 40.
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