Suppose that there are teams: and . Team 's pitcher throws a strike of the time and a ball of the time (successive pitches are independent from one another), and the pitcher never hits the batter. Knowing this, Team 's manager instructs the first batter not to swing at anything. Calculate the following probabilities:

(a) The batter walks on the fourth pitch.

So

(b) The batter walks on the sixth pitch (so two of the first five must be strikes).

So

(c) The batter walks

So this is the same as

(d) The first batter scores while no one is out. Not sure how to do this one.