P(B)=0.2 P(A|B)=0.7 P(B')=0.8 AND P(A|B')=0.9 FIND P(B|A)

Let P(A&B')=w, P(A&B)=x, P(A'&B)=y, P(A'&B')=z, 



then 

(1)   w+x+y+z=1

(2)   P(B)= x+y = 0.2

(3)   P(A|B) = x/(x+y) = 0.7

(4)   P(B') = w+z = 0.8

(5)   P(A|B') = (w+x)/(w+z) = 0.9

From (1) and (2), 

(6)  w+z = 0.8 

From (2) and (3),

 get 

(7)  x=0.14

(8)  y=.06

From (4) and (5)

(9)  w+x = 0.72

from (7) and (9)

(10) w = 0.58

From (6) and (10)

(11) z = 0.22 



P(B|A) = x/(x+w) = 0.14/(0.14+0.58) = 0.14/0.72 = 14/72 = 7/36

Edwin