Question

Stew has a pitching algorithm that never changes. In the first pitch of each plate appearance, he throws a fastball 70% of the time. The following pitch selection is determined *only* by the type of pitch immediately preceding it. If the previous pitch was off-speed, he will throw a fastball 80% of the time and an off-speed pitch 20% of the time. If the previous pitch was a fastball, however, he will throw either a fastball or off-speed pitch with 50% probability. In your excitement to see Stan pitch, you spilled your soda in the concourse and missed the first two pitches of his first plate appearance of the game. You are able to see that his third pitch is an off-speed pitch. Given this information, what is the probability that the first pitch was an off-speed pitch?

Answer 1