Hey tttcomrader.

Recall that p >= 0 so the minimum of (p,1-p) will always be less than 1 - p.

As a consideration of all possibilities let p < 1 - p this means p < 0.5. Now consider 1 - p < p This means p > 0.5.

So if 1 - p is not the minimum then p is the minimum, but this is always less than 1 - p so the inequality still holds.