Home
Class 12
MATHS
A and B are two events such that P(A)!=0...

A and B are two events such that `P(A)!=0.` Find `P(B|A)` , if (i) A is a subset of B (ii) `AnnB=varphi`

Text Solution

Verified by Experts

The correct Answer is:
N/a
(i) Given A is a subset of seb B i.e.
`AsubBimpliesAnnB=A`
`P(AnnB)=P(A)`
`impliesP(B/A)=(P(BnnA))/(P(A))=(P(A))/(P(A))=1`
(ii) Here `AnnB=phiimpliesP(AnnB)=0`
`:.P(B/A)=(P(BnnA))/(P(A))=0/(P(A))=0`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 13.5|15 Videos

  • MATRICES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exerice|15 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If A and B are two events such that P(A)!=0 and P(B | A) = 1 ; then(A) AsubB (B) BsubA (C) B=varphi (D) A=varphi

If A and B are two events such that P(AnnB)=0. 32 and P(B)=0. 5 , find P(A/B)dot

Knowledge Check

  • A and B are two events such that P(A) ne0 , find P (B/A) if A is a subset of B.

    A
    0
    B
    1
    C
    `1/2`
    D
    None of these

  • If A and B are two events euch that P(A) != 0 and P(B//A)=1 then

    A
    `A sub B`
    B
    `B sub A`
    C
    `B = phi`
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    In each of the Exercises choose the correct answer:If A and B are events such that P(A|B) = P(B|A), then (a) AsubB but A!=B (b) A = B (c) AnnB=varphi (d) P (A) = P(B)

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

    A and B are two events such that P(A)=0.54, P(B)=0.69 and P(AnnB)=0.35 . (i) P(AuuB) (ii) P(A'nnB') (iii) P(AnnB') (iv) P(BnnA')

    If A and B are two events such that P(A)=0.4, P(B)=0.8 and P(B//A)=0.6 , then find: (i) P(AnnB) (ii) P(AuuB) (iii) P(A//B)

    If A and B are independent events such that P(A)=0.3 and P(B)=0.5 , then find the values of: (i) P(AnnB) (ii) P(AuuB) (iii) P(A//B) (iv) P(B//A)

    If A and B are two events such that P(AnnB)=0.3 and P(A'nnB')=0.6 , then the value of P(AnnB' or A'nnB) is equal to

    Home
    Profile