In a Little League baseball game, team A s pitcher throws a strike 50% of the time and a ball 50% of the time, successive pitches are independent of one another, and the pitcher never hits a batter. Knowing this, team B s manager has instructed the first batter not to swing at anything. Calculate the probability that

a. The batter walks on the fourth pitch.

b. The batter walks on  the  sixth  pitch  (so two of the rst ve must be strikes), using a count- ing argument or constructing a tree diagram.

c. The batter walks.

d. The rst batter up scores while no one is out (assuming that each batter pursues a no-swing strategy).