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1) If events A and B are independent on given condition C, then does it implies that those two events A and B are independent without the condition C?

2) If events A and B are independent events, then does it implies that A and B are independent on given condition C?

Please provide explanations for both answers.

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It's useful to think simple examples to formulate the idea in your own words.

1) If you know the probability of head, $p$, of a coin, different tosses are independent, but does it imply that toss 1 and toss 2 are still independent if you hand't known $p$?

2) Would two totally different coin tosses be independent if you had known the number of heads appeared in total?

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  • $\begingroup$ I am clear with the second answer and have some confusion with the first one. Are you trying to explain that toss 1 and toss 2 might be dependent on some other conditions? (because toss 1 and toss 2 are always independent without any condition right?) $\endgroup$ – Hari Krishnan Nov 27 '18 at 7:15
  • $\begingroup$ If you don't know $p$, toss 1 and toss 2 are dependent. Let's say you throw a biased coin 99 times, and you obtained all heads. What would your prediction be for the 100th toss? Doesn't it depend on your previous experiences? Note that you don't know $p$. $\endgroup$ – gunes Nov 27 '18 at 7:18

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