Home
Class 12
MATHS
If A and B are any two events such that ...

If A and B are any two events such that `P(A) + P(B) - P(A a n d B) = P(A)`? then
(A) `P(B | A) = 1`
(B) `P(A | B) = 1`
(C) `P(B | A) = 0`
(D) `P(A | B) = 0`

Text Solution

Verified by Experts

`P(A)+P(B)−P(A and B)=P(A)`
⇒`P(A)+P(B)−P(AnnB)=P(A)`
⇒`P(B)−P(AnnB)=0`
⇒`P(AnnB)=P(B)`
∴`P(A/B)= (P(AnnB))/(P(B))`
= `P(A/B)=(P(B))/(P(B)) =1`
Thus, the correct answer is B.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If A and B are two events such that P(A)>0 and P(B)!=1 , then P(A|B') is ...

If A and B are two events such that P(AnnB)=0. 32\ a n d\ P(B)=. 5 , thenP(A//B)

Knowledge Check

  • If A and B are any two events such that P(A) + P(B) - P (A and B) = P(A) , then

    A
    `P (B | A) = 1 `
    B
    `P(A | B ) = 1 `
    C
    `P (B | A) = 0 `
    D
    `P (B | A) = 0 `

  • If A and B are any two events such that P(A)+P(B)-P( A "and" B)=P(A) , then:

    A
    `P(B//A)=1`
    B
    `P(A//B)=1`
    C
    `P(B//A)=0`
    D
    `P(A//B)=0`

  • If A and B are two events such that P(A) ne0 and P(B//A)=1, then :

    A
    `A sub B`
    B
    `B sub A`
    C
    `B = phi`
    D
    `A=phi`

    • Similar Questions

    Explore conceptually related problems

    If A and B are two events such that P(A)=0.6, P(B)=0.5 and P(B/A)=0.4 , then find P(A nn B')

    If A and B are two events such that P(A)=0.5,P(B)=0.6 and P(A uu B)=0.8 ,find P(A/B) and P(B/A) .

    If A and B are two events such that P(A)ne0 and P(B//A)=1 , then :

    If A and B are events such that P(A)= 0.4 , P(B) =0,8 " and " P(B//A) =0.6 then P(A//B)=?

    If A and B are two events such that P(A) ne 0 and P(B) ne 1 then P((barA)/(B))

    Home
    Profile