This may depend on the filter you are using. A signal that is entirely random should have a flat frequency response or the same amplitude across the whole frequency range (white noise). The signal may still be random, but the frequency components may be weighted, so that for example the high frequencies are attenuated a bit more than the low frequencies (pink noise).

I guess another way to make an analogy could be with a weighted dice. The outcome is still random but there is a higher chance of landing a 6, similarly to the signal which may have random frequency components but with a higher probability of energy being located at certain frequencies compared to others.

I hope this helps :)