If `P(A)=P(A//B)=(1)/(4) and P(B//A)=(1)/(2)`, check whether the following statements are true or false:
(a) A and B are mutually independent and
(b) `P(A^(c )//B)=(3)/(4)`.

A and B are mutually independent implies P(AIB) = P(A).

For two events A and B , if P(A)=P((A)/(B))=(1)/(4) and P((B)/(A))=(1)/(2) , then which of the following is not true ?

If P(A)=(1)/(4),P(B)=(1)/(3) and P(A-B)=(1)/(6) , examine whether events A and B are independent.

If P(A//B)=(1)/(3), P(B)=(1)/(4) and P(A)=(1)/(2) , find the probability that exactly one of the events A and B occurs.

A and B are two events defined as follows: A:It rains today with P(A)=40 % B: It rains tomorrow with P(B)=50 % Also, P (it rains today and tomorrow) =30 % Also, E_1: P(AnnB)//(AuuB) and E_2: P({(Ann barB )or(Bnn barA )}//(AuuB)) . Then which of the following is/are true ? (a) A and B are independent events (b) P(A//B) (c) E_1 and E_2 are equiprobable (d) P(A/(AuuB))=P(B//(AuuB))

If P(A)=1/4,P(B)=1/3 and P(A-B)=1/6 then verify whether a and B are two independent event or not.

If P(A)=(3)/(7), P(B)=(4)/(7) and P(A cap B)=(2)/(9) , then the value of P(A//B) is -

A and B are two events, not mutually exclusive, connected with a random experiment E. If P(A)=(1)/(4), P(B)=(2)/(5) and P(A cup B) =(1)/(2) , find the values of the following probabilities : (i) P(A cap B) (ii) P (A cap B^(c )) (iii) P(A^(c ) cup B^(c ))

P(A)=1/2 ,P(B)=2/5 and P(A cup B) =0.7 state whether the events A and B are mutually exclusive

Given P(A)=(3)/(7), P(B)=(4)/(7) and P(A+B)=(7)/(9) for two events A and B. Find P(A//B) and P(B//A) . Are the events A and B independent ?