Question

A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. Find `P(A)` , it being given that `P(B)=3/2P(A)a n dP(C)=1/2P(B)dot`

Answer 1

`P(AnnB)=0`
`P(AnnC)=0`
`P(BnnC)=0`
`P(AuuBuuC)=1`
`P(AnnBnnC)=0`
`P(AuuBuuC)=P(A)+P(B)+P(C)+P(AnnB)+P(AnnC)+P(BnnC)+P(AnnBnnC)`
`P(AuuBuuC)=1=P(A)+P(B)+P(C)`
`1=P(A)+3/2P(A)+1/2P(A)`
`1=P(A){1+3/2+3/4}`
`1=13/4P(A)`
`P(A)=4/13`.