Consider a manager who faces uncertainty regarding which of his employees, if any, will be the first to disturb him in his office before lunch. The state space is given by ?={Ben,Jane,Kate,Nobody}S={Ben,Jane,Kate,Nobody}. Use the proper notation to describe each of the following events (described here in words): A man is first to enter. Neither woman is the first to enter. Someone with an 'n' in their name is first to enter (to clarify, "Nobody" is not a person's name). Now suppose you are at a racetrack and about to bet on a horse race. Let ??sj denote the state in which horse j wins the race. For simplicity, suppose there are just 3 horses, and by studying the form guide, you've concluded that the probabilities of each state are given by  ?(?1)=12,?(?2)=14,?(?3)=14P(s1)=12,P(s2)=14,P(s3)=14. Write down the definition for two events to be independent and explain whether or not ?1s1 and ?2s2 are independent

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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  1. Consider a manager who faces uncertainty regarding which of his employees, if any, will be the first to disturb him in his office before lunch. The state space is given by ?={Ben,Jane,Kate,Nobody}S={Ben,Jane,Kate,Nobody}. Use the proper notation to describe each of the following events (described here in words):
    • A man is first to enter.
    • Neither woman is the first to enter.
    • Someone with an 'n' in their name is first to enter (to clarify, "Nobody" is not a person's name).
  2. Now suppose you are at a racetrack and about to bet on a horse race. Let ??sj denote the state in which horse j wins the race. For simplicity, suppose there are just 3 horses, and by studying the form guide, you've concluded that the probabilities of each state are given by 
    ?(?1)=12,?(?2)=14,?(?3)=14P(s1)=12,P(s2)=14,P(s3)=14.
    Write down the definition for two events to be independent and explain whether or not ?1s1 and ?2s2 are independent.  
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