Suppose a baseball pitcher throws fastballs 80 of the time a

Suppose a baseball pitcher throws fastballs 80% of the time and curveballs 20% of the time. A batter hits a home run on 8% of all fastball pitches and on 5% of all curveball pitches. What is the probability that this batter will hit a home run on this pitcher’s next pitch?

Solution

By Bayes\' Rule,

P(homerun) = P(fast) P(homerun|fast) + P(curve) P(homerun|curve)

= 0.80(0.08) + 0.20(0.05)

= 0.074 [ANSWER]