Let A and B be two events such that `P(AnnB')=0.20,P(A'nnB)=0.15,P(A'nnB')=0.1`thenP(A//B)` is equal to

Options

A. `11//14`
B. `2//11`
C. `2//7`
D. `1//7`

Answer

A

Explanation

`P(AnnB)=P(B)-P(AnnB)=0.20`
Also `P(A'nnB'=P(B)-P(AnnB)=0.15`
`impliesP(A)+P(B)-2P(A-B)=0.35`
Now `P(A'nnB')=1-P(AuuB)`
`implies0.1=1-1 P(A)-P(B)+P(AnnB)`
`impliesP(A)+P(B)-P(AnnB)=0.9`
`impliesP(AnnB)=0.9-0.35=0.55`
`andP(A)=0.75,P(B)=0.70`
Now, ``P(A//B)=(p(AnnB))/(P(B))=(0.55)/(0.70)`