Calculating SNR after lowpass filtering
This looks like an exam/homework style question. If it is, it may be helpful if you could provide a bit of background about what are you expected to know, because there are several ways we could solve this.

The most general way would be to get the power-spectral density of the noise. Then we would integrate it over our bandwidth and get the initial power of the noise. 

Next we have the noise filtering itself. You convolve the noise with the filter in time domain or you multiply the filter's transfer function with the noise PSD in frequency domain. Then you could integrate the surface under the PSD in frequency domain and get noise power.  In the end you get something like in the illustration:



Black rectangle is the PSD of "unfiltered" noise and the red rectangle is the PSD of filtered noise, assuming a filter with square transfer function and AWGN.

In the case of pink noise, the main difference is that the PSD of the noise will look a bit different. Instead of square, you'll get something that looks like a triangle. The procedure is same. You multiply the PSD of the noise with the transfer function of the filter and get a shape. Surface of that shape is your noise power.