Question 1196848: In a year group of 63 students, 22 study biology, 26 study Chemistry and 25 study Physics. 18 study both Physics and
Chemistry, four study Biology and Chemistry and three study both Physics and Biology. One studies all three subjects. How
many students study:
a) Biology only
b) Physics or Chemistry
c) None of Biology, Physics or Chemistry
d) Physics but not Chemistry?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
In a year group of 63 students, 22 study biology, 26 study Chemistry and 25 study Physics.
18 study both Physics and Chemistry, four study Biology and Chemistry and three study both Physics and Biology.
One studies all three subjects.
How many students study:
a) Biology only
b) Physics or Chemistry
c) None of Biology, Physics or Chemistry
d) Physics but not Chemistry?
~~~~~~~~~~~~~~~~
(a) n(B_only) = n(B) - n(B ∩ C) - n(B ∩ P) + n(B ∩ C ∩ P) = 22 - 4 - 3 + 1 = 16. ANSWER
(b) n(P U C) = n(P) + n(C) - n(P ∩ C) = 25 + 26 - 18 = 33. ANSWER
(c) First calculate the union n(B U C U P) using the Inclusive-Exclusive principle formula
n(B U C U P) = n(B) + n(C) + n(P) - n(B ∩ C) - n(B ∩ P) - n(C ∩ P) + nn(B ∩ C ∩ P) =
= 22 + 26 + 25 - 4 - 3 - 18 + 1 = 49.
Now the anwer to (c) is the complement of 49 to 63, or 63-49 = 14. ANSWER
(d) n(P \ (P ∩ C) ) = n(P) - n(P ∩ C) = 25 - 18 = 7. ANSWER
Solved.
|
|
|
