In the game of baseball, every time a player bats, he is  either successful (gets on base) or he fails (doesn’t get  on base). (This is all you need to know about baseball  for this problem!) His on-base percentage, usually  expressed as a decimal, is the percentage of times he is  successful. Let’s consider a player who is theoretically  a 0.3 7 5 on-base batter. Specifically, assume that each  time he bats, he is successful with probability 0.3 7 5 and  unsuccessful with probability 0.625. Also, assume that he bats 600 times in a season. What can you say about  his on-base percentage, (# of successes)/600, for the  season?  a. What is the probability that his on-base percentage  will be less than 0.3 60? b. What is the probability that his on-base percentage  will be greater than 0.3 7 0? c. What is the probability that his on-base percentage  will be less than or equal to 0.400?

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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In the game of baseball, every time a player bats, he is 
either successful (gets on base) or he fails (doesn’t get 
on base). (This is all you need to know about baseball 
for this problem!) His on-base percentage, usually 
expressed as a decimal, is the percentage of times he is 
successful. Let’s consider a player who is theoretically 
a 0.3 7 5 on-base batter. Specifically, assume that each 
time he bats, he is successful with probability 0.3 7 5 and 
unsuccessful with probability 0.625. Also, assume that he bats 600 times in a season. What can you say about 
his on-base percentage, (# of successes)/600, for the 
season? 


a. What is the probability that his on-base percentage 
will be less than 0.3 60?
b. What is the probability that his on-base percentage 
will be greater than 0.3 7 0?
c. What is the probability that his on-base percentage 
will be less than or equal to 0.400?

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