If P(B)`=(3)/(4)` P(A cap B cap overset(-)(c ))=(1)/(3)` and `P(overset(" "-)(A) cap B cap overset(-)(C ))=(1)/(3)`, then `P(B cap C)` is equal to

Question

If P(B)= 3 4 P(A cap B cap overset(-)(c ))=(1)/(3)andP(overset(" "-)(A) cap B cap overset(-)(C ))=(1)/(3),thenP(B cap C)isequal→A.(1)/(2)B.(1)/(6)C.(1)/(15)D.(1)/(9)` Select the correct answer from above options

Answer 1

Correct Answer - A We have, P( ˉ A ∩B∩ ˉ C )= 1 3 ⇒P((B∩ ˉ C )∩ ˉ A )= 1 3 ⇒P(B∩ ˉ C )-P((B∩ ˉ C )∩A)= 1 3 [∵P(X∩ ˉ Y )=P(X)-P(X∩Y)] ⇒P(B∩ ˉ C )-P(A∩B∩ ˉ C )= 1 3 ⇒P(B∩ ˉ C )- 1 3 = 1 3 ⇒P(B∩ ˉ C )= 2 3 ⇒P(B)-P(B∩C)= 2 3 ⇒P(B∩C)=P(B)- 2 3 = 3 4 - 2 3 = 1 12