Respuesta :
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 is 0.57
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Number of bats = 369
Number of hits = 127
Number of home runs = 21
The probability of a hit:
[tex]=\frac{127}{369}[/tex] (includes home run)
The probability of home run:
[tex]=\frac{21}{369}[/tex]
The probability of hit run(without home run)
[tex]=\frac{127}{369}-\frac{21}{369}[/tex]
[tex]=\frac{106}{369}[/tex]
The probability of no hit:
[tex]=\frac{369-127}{369}[/tex]
[tex]=\frac{242}{369}[/tex]
For home run, the score will be 5 points.
If not, a home run score will be 1 points.
If Miguel does not get hit, score will be zero point.
Expected value of Miguel hit at each bat is (without home run):
For 5 hit:
[tex]=\frac{106}{369}[/tex]
For 21 home runs, the points will be 21×5 = 105 (5 points for each home run)
The expected value for this:
[tex]\frac{105}{369}[/tex]
Adding both expected hits, we get:
[tex]=\frac{106}{369}+\frac{105}{369}[/tex]
[tex]=\frac{211}{369}[/tex]
= 0.571 ≈ 0.57
Thus, 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 is 0.57
Learn more about the probability here:
brainly.com/question/11234923
