# 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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oobleck

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3. is the person answering the question above?

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4. In a class,30 offer biology,21 offer are chemistry and 22 offer are physics.15 offer physics and biology,10 offer physics and chemistry and 13 offer biology and chemistry,2 offer physics only,5 offer chemistry only,and 7 offer biology only.(I)illustrate this information in a Venn diagram.(ii)find the number of students.(a)who offer all the three subjects.(b)in the class.(c)if a student s sellected at random what is the probability that is studies either physics or chemistry.

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