SOLUTION: Suppose a baseball pitcher throws fastballs 80% of the time and curveballs 20% of the time. Suppose a batter hits a home run on 8% of all fastball pitches, and on 5% of all curve

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose a baseball pitcher throws fastballs 80% of the time and curveballs 20% of the time. Suppose a batter hits a home run on 8% of all fastball pitches, and on 5% of all curve      Log On


   

Question 1119032: Suppose a baseball pitcher throws fastballs 80% of the time and curveballs 20%
of the time. Suppose 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?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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%.