Mathematics

In a class,30 offer Biology,21 offer Chemistry and 22 offer Physics.15 offer Physics and Biology,10 offer Physics and Chemistry and 13 offer Biology and Chemistry.2 offer Physics only,3 offer Chemistry only and 7 offer Biology only.
a.illustrate this information in a Venn diagram
b.find the number of students
i.who offer all the three subjects
ii.in the class
C.If a student is selected at random, what is the probability that he studies either Physics or Chemistry.

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  1. draw the Venn diagram. It is easy to fill in
    2 offer Physics only,3 offer Chemistry only and 7 offer Biology only.
    Now if we let
    x = only Biology and Chemistry
    y = only Biology and Physics
    z = only Chemistry and physics
    a = all three
    Then we have
    x+y+7+a = 30
    x+z+3+a = 21
    y+z+2+a = 22
    There is no unique solution, since we do not know how many students there are in the class. But the above equations tell us that
    y = x+2 = z+5
    So some solutions are
    x y z a Class
    4 6 1 13 36
    5 7 2 11 37
    ...
    10 12 7 1 42

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