Random Turns

You are driving north in a city whose streets form a perfect grid (every street runs north-south or east-west). At each of your next several intersections you turn left or right, each with probability $1/2$ independently, so you always turn (never go straight).

Give two probabilities, in this order: (1) the probability you are driving north after 10 turns, and (2) the probability you are driving north after 57 turns. Answer as two decimal numbers separated by a comma.