Mentally add the probe and collector capacitance of about 5pF in parallel with the collector load resistor. That gets you a 4.7k * 5pF time constant, or a cutoff frequency no higher than 6.7MHz. Which will be lower with Miller effect, of course.
To address the capacitance, you have to use smaller load resistances. Which will draw more current. So like, R4 = 47, R3 = 220. And R1-R2 will have to be lower as well, since base current will be higher. This raises bandwidth (and shortens battery life!) proportionally.
To get around Miller effect, you can use a grounded base amplifier, or a combo that contains one, like a cascode or diff pair type circuit. The disadvantage to these is, more transistors in series means less voltage available for your output signal.
You can also isolate the load (probe) capacitance with a buffer. An emitter follower is excellent for this.
At very high frequencies (meaning, a low end of perhaps MHz, on up to... anything), it is convenient to replace many resistors with transformers and inductors, so that those resistors aren't loading down the signal. If you only need a narrow frequency range, you can skimp even further and use too-small inductors for the replacement, resonating them with capacitors to preserve performance. Now you have a tuned RF amplifier.
Tim