1.

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)//bar(A))`

Answer» We have :
(i) `P(A//B)=(P(Ann B))/(P(B))=((1//5))/((1//4))=(1/5xx4/1)=4/5`.
(ii) `P(B//A)=(P(B nn A))/(P(A))=(P(A nn B))/(P(A))=((1//5))/((1//3))=(1/5xx3/1)=3/5`.
(iii) `P(A uu B)=P (A)+P(B)-P(A nn B)`
`=(1/3+1/4-1/5)=((20+15-12))/(60)=23/60`.
(iv) `P(bar(B)//bar(A))=(P(bar(B) nn bar(A)))/(P(bar(A)))=(P (bar(A) nn bar(B)))/(P(bar(A)))=(P(bar(A uu B)))/(P(bar(A)))`
`=(1-P(Auu B))/(1- P(A))=((1-23/60))/((1-1/3))=((37/60))/((2/3))=(37/60xx3/2)=37/40`.


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