If `A` and `B` are two independent events such that `P( barA nnB)=2//15` and `P(Ann barB )=1//6`, then `P(B)` is

Options

A. `1//5`
B. `1//6`
C. `4//5`
D. `5//6`

Answer

B, C

Explanation

Let `P(A)=xand P(B)=y.` Since A and B are independent events, therefore,
`P(barAnnB)=2//15`
`impliesP(barA)P(B)=2//15`
`implies(1-P(A))P(B)=2//15`
`implies (1-x)y=22//15" "(1)`
and `P(AnnbarB)=1/6=1/6impliesP(A)P(barB)=1/6`
` implies x(1-y)=1/6`
`impliesx=xy=1/6" "(2)`
Subtracting Eq. (1) from Eq. (2), we get
`x-y=1/30impliesx=1/30+y`
Putting this value of x in Eq. (1). We get
`y-y((2)/(30)+y)2/15`
`or 30y-y-30y^(2)=2//5`
`or30y^(2)-29y+4=0`
`or(6y-)(5y-4)=0`
`impliesy=1//6or y=4//5`
`implies P(B)=1//6orP(B)=4//5`