Home
Class 12
MATHS
If A and B are exhaustive events in a sa...

If `A` and `B` are exhaustive events in a sample space such that probabilites of the events `AnnB`, `A`, `B` and `AuuB` are in `A.P.` If `P(A)=K`, where `0 lt K le 1`, then

A

`P(B)=(K+1)/(2)`

B

`P(AnnB)=(3K-1)/(2)`

C

`P(AuuB)=1`

D

`P(A'uuB')=(3(1-K))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`(a,b,c,d)` `A`, `B` are exhaustive events `implies AuuB=S`
`impliesP(AuuB)=1`
`2P(B)=P(A)+P(AuuB)=K+1`
`impliesP(B)=(K+1)/(2)-P(AuuB)-P(A)-P(B)`
`=-1K-((K+1))/(2)=(2-2K-K-1)/(2)`
`:. P(AnnB)=(3K-1)/(2)`
`P(A'uuB')=P((AnnB)')`
`=1-P(AnnB)`
`=1-(3K-1)/(2)`
`=(3(1-K))/(2)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    CENGAGE|Exercise Single correct Answer|46 Videos

  • PROBABILITY

    CENGAGE|Exercise Comprehension|2 Videos

  • PROBABILITY

    CENGAGE|Exercise Comprehension|2 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE|Exercise Exercise|9 Videos

  • PROBABILITY AND STATISTICS

    CENGAGE|Exercise Question Bank|24 Videos

Similar Questions

Explore conceptually related problems

Let S and T are two events difined on a sample space with probabilities P(S)=0.5,P(T)=0.69,P(S//T)=0.5 Events S and T are

If A and B are mutually exclusive events and S is the sample space such that P(A)=(1)/(3) P(B) and S=AuuB , then P(A)= .............

Let S and T are two events defined on a sample space with probabilities P(S)=0.5,P(T)=0.69,P(S//T)=0.5 The value of P(S and T) is

If A and B are events such that P(A|B)= P(B|A), then

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

The probablities of events , AnnB , A , B and AuuB are respectively in A.P. with second term equal to the common difference. Therefore A and B are

A and B are events of an experiment such that 0 lt P(A) , P(B) lt 1 . If P(B') gt P(A') , then

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