Home
Class 12
MATHS
If A, B are two events, then show that ...

If A, B are two events, then show that
(i) `P((A)/(B))P(B)+P((A)/(B^(C )))P(B^(C ))=P(A)`
(ii)`P(A^(c )|B^(c ))=(1-P(AuuB))/(1-P(B)),P(A) gt 0, P(B) ne 1`
(iii) `P(A//B^(C ))=(P(A)-P(AnnB))/(-P(B)),P(B^(C )) gt 0`

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    AAKASH SERIES|Exercise Exercise 2.3(short answer type question)|11 Videos

  • PROBABILITY

    AAKASH SERIES|Exercise Exercise 2.3(long answer type question)|9 Videos

  • PROBABILITY

    AAKASH SERIES|Exercise Exercise 2.2(short answer type question)|8 Videos

  • PERMUTATIONS & COMBINATIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|163 Videos

  • QUADRATIC EQUATIONS & EXPRESSIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|88 Videos

Similar Questions

Explore conceptually related problems

If A,B are two events, then show that P((A)/(B))P(B)+P((A)/(B^(C)))P(B^(C))=P(A).

For any two events A,B shows that P(AcapB)-P(A)P(B)=P(A^(C))P(B)-P(A^(C)capB) =P(A)P(B^(C))-P(AcapB^(C))

If A and B are any two events of a random experiment then show that (i) P(A^(C) nn B^(C)) = P(A^(C)) - P(B) "if A" nn B = phi (ii) P(A^(C)//B^(C)) = (1-P(A uu B))/(1-P(B)) "with P(A)" ne 0 and P(B) ne 1

If A and B are two events such that P(A)=1//4, P(B)=1//2, P(uuB)=5//8 then P(A nn B) =

For any two events A and B, shows that P(A^(C)capB^(C))=1" +"P(AcapB)-P(A)-P(B).

If A and B are two events such that P(A|B)=0.6 , P(B|A)=0.3 , P(A)=0.1 then P(barAnnbarB)=

If A and B are two events such that P(A uu B)=0.65, P(A nnB)=0.15 then P(barA)+P(barB) =

If A and B are two events such that P(A) = 0.3 , P(B) =0.6 and P(B|A) = 0.5 , then P(A|B) =