Finding probablity

Question

Miguel Cabrera has had 369 at bats, and he has 127 hits and 21 home runs. (Note: The home runs are included in the hits data.) If he is challenged to a batting battle, what is the expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run?

Answer 1

AJ,

 

The probability of a hit is 127/369 This includes home runs.

The probability of a home run is 21/369 = 7/123

The probability of a hit that is not a home run is (127-21)/369 = 106/369

The probability of no hit is (369-127)/369 = 242/369

 

Now,

If Miguel hits a home run, he'll score 5 points

If Miguel has a hit that is not a home run, he'll score 1 point

If Miguel does not get a hit, he'll score 0 points.

 

Expected value of his score at each at bat is

(0) 242/369 + (1) 106/369 + (5) 21/369

106/369 + 105/369 = 211/369 = .572