If `P(A//B)=1` then prove that, `P(ABC)=P(BC)`.

If P(A//C) geP(B//C) P(A//barC) geP(B//barC) , then prove that, P(A)geP(B) .

Prove that P(A^C) = 1 - P(A)

If A and B are two events such that P(A) = P(B) = 1, then show that , P(A+B) = 1, P(AB) = 1

If A and B are two events., such that P(A) = P(B)-= 1, then Prove that P(A + B)= 1.

If P(A//B)=P(A//B ') , then prove that A and B are independent.

If A and B are two events and P(B) ne 1 , prove that, P(A//B^(c ))=(P(A)-P(A cap B))/(1-P(B)) Hence, deduce that, P(A cap B) gt P(A) +P(B)-1 .

If P(A) = 1/2, P(B) = 2/3 then prove that 1/6 le P(A nn B) le 1/2

If P(A) = 1/2, P(B) = 2/3, then prove that 1/6 le P(A nn B) le 1/2 .

If P(B/A)=P(B/(A ')) , then prove that A and B are independent.

The equilateral triangle ABC is inscribed in a circle. If P is any point on the ar BC, then prove that AB=PB+PC .