# Conditional independence of two events

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?

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 $$p$$?
• 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 $p$. – gunes Nov 27 '18 at 7:18