If `A ,B ,C` be three mutually independent events, then `Aa n dBuuC` are also independent events. Statement 2: Two events `Aa n dB` are independent if and only if `P(AnnB)=P(A)P(B)dot`

Each of the following question contain two statements- Statemnet I and statement II. Each of the questions has following four choice A,B,C and D only one of which is correct. Statement- I: If A,B,C the three mutually independent events, then A and B cup C are also independent events. Statement- II: Two evetns A and B are independent if and only if P(AcapB)= P(A).P(B)

If A, B and C are mutually independent events, prove that the events (A cup B) and C are also independent events.

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.

If events A and B are independent, then so are A^c and B?

Let Aa n dB be two independent events. Statement 1: If P(A)=0. 4a n dP(Auu barB )=0. 9 ,t h e nP(B)i s1//4. Statement 2: If Aa n dB are independent, then P(AnnB)=P(A)P(B)dot .

If A and B are independent events, then P(A/B^C) = …………..

Let A ,B ,C be three mutually independent events. Consider the two statements S_1 and S_2 . S_1 : A and BuuC are independent S_2 : A and BnnC are independent. Then,

If A and B are two mutually exclusive event then P(A-B) =

If the events A^C and B^C are independent then show that A and B are independent.