Vb = (Vcc X R2bg)/(R1+R2bg) = (15V X 4.87KΩ)/(47KΩ + 4.87KΩ) = 1.41V
Using these values to calculate Ibe is
Ibe = Vb / Base to Ground resistance = 1.41V/110KΩ = 12.8ua
Again, since β is such a variable these values can vary a bit. And this doesn't even count other variables, like tolerances of the resistors. The exact Base Emitter drop is also a major variable, but I was taught in school to round off to .7V. The reality is it is between .6 and .7V, depending on transistor family type.
These equations work, but they only get you in the ball park. Sometimes there is no substitute to building a prototype to pin it down, and if you're parts have a wide tolerance like the 10% resistors, there can still be problems. The Vbe is pretty tight within a family of transistors, which helps.