Question 1119032
pitcher throws fast ball 80% of the time and curve ball 20% of the time.


batter hits a home run on 8% of fast ball pitches and 5% of curve ball pitches.


the probability that the batter will hit a home run the next time at bat should be:


.08 * .8 + .05 * .2 = .074 = 7.4% of the time.


let's assume the pitcher pitches to this batter 1000 times.


80% of the time he will pitch a fast ball = 800 pitches.


20% of the time he will pitch a curve ball = 200 pitches.


the batter hits a home run 8% of 800 pitches = 64 times.


the batter hits a home run 5% of the 200 pitches = 10 times.


out of the 1000 pitches, the batter hits a home run 74 times.


74 / 1000 = .074 = 7.4%.