Determining average number of hash calls to get a hash that begins with X
Assuming the output is uniformly random, the probability of any given bit being 0 is $\frac{1}{2}$. So the probability that $b_0,b_1,b_2...b_{14} = 0$ is ${(\frac{1}{2}})^{15}$.

On average, it will require $2^{15}$ calls to find a hash where the first 15 bits are 0.