Let A and B be two non-null events such that `A sub B`. Then, which of the following statements is always correct.

Options

A. `P(A//B)=P(B)-P(A)`
B. `P(A//B) geP(A)`
C. `P(A//B) leP(A)`
D. `P(A//B)=1`

Answer

B

Explanation

We know that , `P(A//B)=(P(A cup B))/(P_(B))`
[ by the definition of conditional probability ]
`:' A sub B `
`implies A cap B =A `
`:. P(A//B) =(P(A))/(P_(B))`
As we known that , ` 0 le P(B) le 1`
`:. 1 le (1)/(P(B)) lt oo implies P(A) le (P(A))/(P_(B)) lt oo`
`implies (P(A))/(P(B)) ge P(A)`
Now , from Eqs (i) and (ii) , we get
`P(A// B) ge P(A) `
Now , from Eqs (i) and (ii) , we get
`P(A//B) ge P(A)`