Suppose you flip a coin n times, and the probability of getting heads 15 times is .0148. what n?

With n tosses, there are a total of 2^n possible outcomes. We need 15 of theses to be heads.
Since the tosses are random, we want to count the ways to have exactly 15 of them being heads. That will be C(n,15) ways to pick which tosses are heads.
The probability will be given by:
C(n,15)/2^n=0.0148
At this point we use various values of n until we get the correct probability.
n=18⇒0.003112793
n=19⇒0.007392883
n=20⇒0.014785767
n=21⇒0.025875092

n=20