1. a coin is tossed until a tail appears. what is the probability that a tail will appear in at most 5 tries

You have have to add up probabilities of it appearing on 1,2,3,4,5 tries. So t=1/2, ht=1/4,hht=1/8, hhht=1/16,t=1/32. You add up all those probabilities and that is the pr(X less than equal to 5) for x=1,...5