SOLUTION: Jogn was trying to find out who in the Kansas City area liked the Philadelphia Phillies and the Kansas City Royals baseball teams. He interviewed 150 people. He found that: -

In this case, Venn diagram consists of two intersecting circles, concluded into larger rectangle.


One circle represents those 83 who like P.


The other circle represents those 107 who like R.


The intersection of circles represents those 54 who like both.


The entire rectangle represents those 150 who were interviewed.


As soon as you will draw the sketch of the diagram, the solution is clear to you:


    a. How many liked only the Phillies?                          83 - 54 = 29.

    b. How many liked only the Royals?                           107 - 54 = 53.

    c. How many did not like either the Phillies or the Royals?  150  - 83 - 107 + 54 = 14.


Only the last calculation requires some explanation  (the "a" and "b" are OBVIOUS).


To calculate those inside the rectangle, who don't like  P or R, we subtract the population of both circles from the rectangle.

But since we subtract the intersection TWICE, we are oblige to add the value of this intersection one time.