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

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

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.

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^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?

If A and B are two independent events, prove that the events (a) a^(c ) and B^(c ) (b) A^(c ) and B (c ) A and B^(c ) are also independent.

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) = …………..