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?
a) 0.36
b) 0.43
c) 0.57
d) 0.63

The answer is C.

The probability of a hit is 127/369 This includes home runs.The probability of a home run is 21/369 = 7/123The probability of a hit that is not a home run is (127-21)/369 = 106/369The probability of no hit is (369-127)/369 = 242/369 Now,If Miguel hits a home run, he'll score 5 pointsIf Miguel has a hit that is not a home run, he'll score 1 pointIf 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) 21/369106/369 + 105/369 = 211/369 = .57