If `Aa n dB` are two independent events such that `P(A)=1//2 a n d P(B)=1//5,` then

Options

A. `P(A//B)=1//2`
B. `P((A)/(AuuB))=5/6`
C. `P((AnnB)/(A'uuB'))=0`
D. None of these

Answer

A, B, C

Explanation

`P(A//B)=P(A)=1/2`
`P{A//(AuuB)}=(P[Ann(AuuB)])/(P(AuuB))`
`" "[becauseAnn(AuuB)=Ann(A-B-Ann)]`
`=A-AnnB-AnnB=a}`
`impliesP((A)/(AuuB))=(P(A))/(P(AuuB))`
`=(1/2)/(1/2-1/5-1/10)=(1/2)/(6/10)=5/6`
and similarly,
`P((AnnB)/(A'uuB'))=0`