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

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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Question

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.

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