Let A and B be two events such that `P(A)=0.3,P(B)=0.4` and `P(A^(')capB^('))=0.4` which of following is/are correct?

Options

A. `P((A)/(overline(B)))=(1)/(3)`
B. `P((B)/(overline(A)))=(4)/(7)`
C. A and B are independent events
D. `A^(')` and `B^(')` are not independent events

Answer

A, D

Explanation

`P(A)=0.3,P(B)=0.4P(A^(')capB^('))=0.4`
`impliesP(AcupB)^(')=0.4`
`impliesP(AcupB)=0.6`
`P(A)+P(B)-P(AcapB)=0.6`
`impliesP(AcapB)=0.1`
`P(A)neP(Acapoverline(B))implies` A&B are not independent events
`P((A)/(overline(B)))=((Acapoverline(B)))/(P(overline(B)))=(P(A)-P(AcapB))/(1-P(B))=(0.2)/(0.6)=(1)/(3)`
`P((B)/(overline(A)))=(P(Bcapoverline(A)))/(P(overline(A)))=(P(B)-P(AcapB))/(1-P(A))=(0.3)/(0.7)=(3)/(7)`