108. 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.

pi 5 P(Gi)

Gi 5 5the target is detected on the ith glimpse6 P(granite) 5 p R3 , R1 , R2 R1 , R3 , R2 R2 , R3 R1 , R2 , R3 )

P(granite | R1 , R2 , R3 P(basalt | R1 , ) .

P(granite) 5 .25 P(basalt) 5 .75 Calculate the probability that

a. The batter walks on the fourth pitch

b. The batter walks on the sixth pitch (so two of the first five must be strikes), using a counting argument or constructing a tree diagram

c. The batter walks

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