Give the condition when two events A and B will be mutually independent?

The number of condition for three events A, B and C are to be mutually independent is

Choose the correct answer Two events A and B will be independent, if

If the events A and B are mutually exclusive then-

A balanced coin is tossed three times in succession. Let A denote the event of getting 'head' in the first toss and B the event of getting 'tail' in the second toss. Prove that the events A and B are independent.

Three unbaised coins are tossed simultaneously. Describe two events A and B which are mutually exclusive,

Let A and B be two events such that p( bar (AuuB))=1/6, p(AnnB)=1/4 and p( bar A)=1/4 , where bar A stands for the complement of the event A. Then the events A and B are (1) mutually exclusive and independent (2) equally likely but not independent (3) independent but not equally likely (4) independent and equally likely

If A and B are two independent events, prove that A^C and B are also independent events.

If A^c and B^c are two independent events, then show that A and B are also independent.

In the random rxperiment of rolling an unbiased die, let A be the event of getting a digit less than 4 and B be then event of getting a digit greater than 3 , show that the events A and B are mutually exclusive and exhaustive.

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