# Independence of flipping a coin

I have a coin that lands on heads with probability $N$ and tails with probability $1-N$. How do I explain the outcomes of the successive flips of the coin are independent of each other, knowing only $N$. Also if I didn't know the value of $N$, are the outcomes of the successive flips of the coin independent of each other?

• That should be "lands heads with probability $N$ and tails with probability $1-N$", yes? – David Feb 18 '14 at 23:14
• comment now redundant – oks Feb 18 '14 at 23:14
• @David Yes, corrected my question now. Thanks. – orange Feb 18 '14 at 23:15
• still $N-1$ instead of $1-N$ – Denis Feb 18 '14 at 23:23
• It's rather unusual to use $N$ for denoting a fractional number. Apart from that, I don't understand the bit about "explain the successive flips of the coin are independent of each other" – leonbloy Feb 18 '14 at 23:33

I'm taking that each coin flip has $\mathbb{P}(\text{heads}) = N$ and $\mathbb{P}(\text{tails}) = 1-N$.
If two events A, B are independent, then $\mathbb{P}(A) = \mathbb{P}(A|B)$. Let $A$, $B$ be two successive coin flips. Then we can see that the coin flips must be independent given the above information.