Wasn't sure which forum to put this in, I've done the probability part - it's just that my answer is a few lines away from the sample solution I've been given, and I don't understand what they've done.

My answer is

The next line of working for the sample solution is

I see that the sqrt(pi) and the gamma(1/2) cancel, other than that I'm stuck! :(

Any help would be much appreciated. not sure if it's needed or not, but k = n/2 where n is an positive even integer