Let a and B be the events such that `P(A)=1/3, P(B)=1/4` and `P(A nn B)=1/5`. Find : (i) `P(A//B)` (ii) `P(B//A)` (iii) `P(A uu B)` (iv) `P(bar(B)//ba

Question

Let a and B be the events such that P(A)= 1 3 ,P(B)= 1 4 and P(A∩B)= 1 5 . Find : (i) P(A/B) (ii) P(B/A) (iii) P(A∪B) (iv) P( ˉ B / ˉ A ) Select the correct answer from above options

Answer 1

We have : (i) P(A/B)= P(A∩B) P(B) = (1/5) (1/4) =( 1 5 × 4 1 )= 4 5 . (ii) P(B/A)= P(B∩A) P(A) = P(A∩B) P(A) = (1/5) (1/3) =( 1 5 × 3 1 )= 3 5 . (iii) P(A∪B)=P(A)+P(B)-P(A∩B) =( 1 3 + 1 4 - 1 5 )= (20+15-12) 60 = 23 60 . (iv) P( ˉ B / ˉ A )= P( ˉ B ∩ ˉ A ) P( ˉ A ) = P( ˉ A ∩ ˉ B ) P( ˉ A ) = P( ¯ A∪B ) P( ˉ A ) = 1-P(A∪B) 1-P(A) = (1- 23 60 ) (1- 1 3 ) = ( 37 60 ) ( 2 3 ) =( 37 60 × 3 2 )= 37 40 .