Find Pr(A∩B′) when Pr(A∪B)=0.8, Pr(A)=0.5 and Pr(B)=0.4

Question

1. Find Pr(A∩B′) when Pr(A∪B)=0.8, Pr(A)=0.5 and Pr(B)=0.4
2. Find Pr(A′ ∩ B) when Pr(A ∪ B) = 0.76, Pr(A) = 0.31 and Pr(B) = 0.59

Answer 1

P(A and not B) = P(A) - P(A and B)

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

0.8 = 0.5 + 0.4 - P(A and B)

P(A and B) = 0.1

P(A and not B) = 0.5 - 0.1 = 0.4

P(not A and B) = P(B) - P(A and B)

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

0.76 = 0.31 + 0.59 - P(A and B)

P(A and B) = 0.14

P(not A and B) = 0.59 - 0.14 = 0.45

Answer 2

Venn diagrams are very useful for these types of problems. Go to the link below for an illustration of question 1 (you have to copy and paste into browser as link is not live).

Try to go slowly, line by line and see how it applies to the Venn diagram. Once you understand you can apply the logic to question 2.

https://drive.google.com/file/d/1rHQM6AxjcSiW2VKbWmBucCEYzXYCszbP/view?usp=sharing