Suppose you are given a coin that lands ${heads}$ with probability $x$
and ${tails}$ with probability $1 - x$. Are the outcomes of successive
flips of the coin independent of each other given that you know the
value of $x$? Are the outcomes of successive flips of the coin
independent of each other if you do not know the value of
$x$? Justify your answer.
Suppose you are given a coin that lands ${heads}$ with probability $x$ and ${tails}$ with probability $1 - x$. Are the outcomes of successive flips of the coin independent of each other given that you know the value of $x$? Are the outcomes of successive flips of the coin independent of each other if you do not know the value of $x$? Justify your answer.