Question

P(A) = 0.41

P(B) = 0.47

P(A ∩ B) = 0.19



Draw a Venn Diagram of rough paper and find P(A' ∪ B).

Answer 1

Answer:

p (A U B)=P (A)+P (B)-P(A ∩ B)

similarly P(A' ∪ B)=P(A')+P (B)-P(A' ∩ B)

=1-P (A)+P (B)-P (A')P (B)

= 1-P (A)+P (B)-[1-P (A)]P (B)

= 1-P (A)+P (B)[1-1+P (A)]

= 1-P(A)+P(B)P(A)

= 1-P (A)[1-P (B)]

= 1-P (A)P (B')

so P (A)=0.41

P (B)=0.47

P (B')=1-0.47=0.53

P (A)P (B')=0.41×0.53=0.2173

1-P (A)P (B')=1-0.2173=0.7827

so P(A' ∪ B)=0.7827