If P(A)=0.7 , P(A and B)=0.3 , P(A or B)=0.8 , then find P(not B)

Question

Probability question

Answer 1

P(A or B) = P(A) + P(B) - P(A and B)

 

So, 0.8 = 0.7 + P(B) - 0.3

 

     P(B) = 0.4

 

     P(not B) = 1 - P(B) = 0.6

Answer 2

0.6 is the answer; this is evident if you draw partially overlapping circles A & B. Place probability 0.3 in the common area (A∩B) and 0.4 in the rest of circle A. Place probability 0.1 in the part of B that excludes the A∩B area. That leaves 0.2 as outside all circles; you have four different probabilities that add up to 1.0.