SOLUTION: Draw a Venn Diagram and use the given information to fill in the number of elements in each region. n(A)=24, n(B)=17 n(AUB)=32 and n(A')=11

Algebra ->  Probability-and-statistics -> SOLUTION: Draw a Venn Diagram and use the given information to fill in the number of elements in each region. n(A)=24, n(B)=17 n(AUB)=32 and n(A')=11      Log On


   

Question 1083879: Draw a Venn Diagram and use the given information to fill in the number of elements in each region. n(A)=24, n(B)=17 n(AUB)=32 and n(A')=11
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


  n(A) = 24 = x + y
  n(B) = 17 = y + z
n(AUB) = 32 = x + y + z
 n(A') = 11 = z + w 

So the system of equations is:

(eq. 1)              x + y         = 24
(eq. 2)                  y + z     = 17
(eq. 3)              x + y + z     = 32
(eq. 4)                      z + w = 11

Subtract (eq. 3) minus (eq. 1)

 (eq. 3)              x + y + z     = 32
-(eq. 1)             -x - y         =-24
----------------------------------------
                              z     =  8

Subtract (eq. 3) minus (eq. 2)

 (eq. 3)              x + y + z     = 32
-(eq. 2)                 -y - z     =-17
----------------------------------------
                      x             = 15

Substitute x = 15 in (eq. 1)
(eq. 1)              15 + y         = 24  
                          y         =  9

Substitute z = 8 in (eq. 4)

(eq. 4)                      z + w = 11
                             8 + w = 11
                                 w = 3



Edwin