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 ,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 and B are two mutually exclusive events, then-

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.

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

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,

Events Aa n dC are independent. If the probabilities relating A ,B ,a n dC are P(A)=1//5, P(B)=1//6; P(AnnC)=1//20 ; P(BuuC)=3//8. Then (a)events Ba n dC are independent (b)events Ba n dC are mutually exclusive events.(c) Ba n dC are neither independent nor mutually exclusive (d)events Ba n dC are equiprobable

Prove that if E and F are independent events, then so are the events E and F'.