If p is a prime and `ab-=0` (mod p) then show that either a=0 (mod p) or `b-=0` (mod p).

Show that the relation R on the set A of points in a plane given by R ={(P,Q): distance of the point P from the origin is same as the distance of the point Q from the origin) is an equivalence relation. Further, show that the set of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.

If P(A/B) gt P(A) then prove that P(B/A) gt P(B)

If A and B are two events such that P(A) = 0.3 , P(B) = 0.4 , P(A uu B)= 0.6 . Find P(A/B) .

For two events A and B, if P(A) =3/4 and P(B)=5/8 Then show that 3/8 le P(A cap B)le 5/8

If A and B are two events such that P(A) = 0.6 , P(B)= 0.5 and P(A nn B)= 0.2 , then find P(A/B^(c)) .

Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find P(A or B).

Let A and B be the independent events with P(A)=0.3 and P(B)=0.4 find P(A//B)

Let A and B be the independent events with P(A)=0.3 and P(B)=0.4 find P(B//A)