Formula for Heads or tails task Someone offers you this:
"We toss a coin and we pick heads or tails. Whenever you are the winner - I give you \$1.1 (one dollar and ten cents).   Whenever I am the winner - you give me \$1 (one dollar).  However, we are obliged to toss exactly 300 times." 
Now the question is the following: what is the probability of you ending up with a loss (no matter big or small) after the 300 tosses and what is the formula to solve this?
Thanks in advance!

Some hints to get you started: 
If I win $k$ times and you win $300-k$ times, then my net profit in dollars is $1.10k - 1.00(300-k)$. 
How big/small does $k$ need to be for this profit to be negative? 
The number of tosses that I win is a binomial distribution with $n = 300$ trials and probability of success $p = \dfrac{1}{2}$. Hence, the probability of me winning exactly $k$ times is $\dbinom{300}{k}\cdot 2^{-300}$. 
Since summing $\dbinom{300}{k}\cdot 2^{-300}$ over several values of $k$ is probably not an easy calculation, you might want to use the fact that for large $n$, the binomial distribution is close to a normal distribution with mean $np$ and standard deviation $\sqrt{np(1-p)}$. 
