We have a special coin. When we flip it: the coin always lands in heads the first time, the second time - tails. Beginning with the third flip (n+1) the probability of getting heads is $\dfrac{m}{n}$ - where n is the number of flips, and m - number of heads obtained in n flips. (i.e if k denotes the number of tails, k+m=n).
For example:
$n=2$, probability of getting heads in the third flip is always $\frac{1}{2}$.
$n=3, (m=2, k=1)$ probability of getting heads in the $4^{th}$ flip in this case $\frac{2}{3}$
$n=3, (m=1, k=2)$ probability of getting heads in the $4^{th}$ flip in this case $\frac{1}{3}$
1) What is the probability of getting 200 heads from this coin after 300 flips?
2) What is the probability of getting A heads from this coin flip B times? (B>A) times?