If two events `A` and `B` are such that `P(A^(l))=0.3`, `P(B)=0.4` and `P(A nn B^(l))=0.5`, then `P(B/(A uu B^(l)))` equals

Explanation

`P(B//A(A uuB'))=(P(Bnn(AuuB')))/(P(AuuB'))`
`=(P[(BnnA)uu(BnnB')])/(P(A)+P(B)-P(AnnB'))`
`=(P(AnnB))/(P(A)P(B')-P(AnnB'))`
Now, `P(A'nnB')=0.5`
`therefore1-P(AuuB)=0.5`
`impliesP(AuuB)=0.5`
`impliesP(A)+P(B)-P(AnnB)=0.5`
`impliesP(AnnB)=0.3+0.4--0.5=0.2`
`P(AnnB')=P(A)-P(AnnB)=0.3-0.2=0.1`
`P(B//(AuuB'))=(0.2)/(0.3+0.6-0.1)=(0.2)/(0.8)=1/4`