Say that you are playing rock-scissors-paper with a friend. You have played with him several times and have realized he usually follows a pattern. So, after playing for a very (very!) long time you have realized that the probability that you win is 8/12, that you tie is 1/12 and that you loose is 3/12. Making use of that piece of information one day you tell him: I will pay $1 for playing with you. If I win I get my $1 back together with $1 from you. If we tie I only get my $1 back. If I loose I give you my $1. la) Compute your expected profit from this bet. Justify your answer. 1b) What is the fair value of this bet? Justify your answer.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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Say that you are playing rock-scissors-paper with a friend.
You have played with him several times and have realized
he usually follows a pattern. So, after playing for a very
(very!) long time you have realized that the probability
that you win is 8/12, that you tie is 1/12 and that you loose
is 3/12.
Making use of that piece of information one day you tell
him:
I will pay $1 for playing with you. If I win I get my $1 back
together with $1 from you. If we tie I only get my $1 back. If
I loose I give you my $1.
1a) Compute your expected profit from this bet. Justify
your answer.
1b) What is the fair value of this bet? Justify your answer.
Transcribed Image Text:Say that you are playing rock-scissors-paper with a friend. You have played with him several times and have realized he usually follows a pattern. So, after playing for a very (very!) long time you have realized that the probability that you win is 8/12, that you tie is 1/12 and that you loose is 3/12. Making use of that piece of information one day you tell him: I will pay $1 for playing with you. If I win I get my $1 back together with $1 from you. If we tie I only get my $1 back. If I loose I give you my $1. 1a) Compute your expected profit from this bet. Justify your answer. 1b) What is the fair value of this bet? Justify your answer.
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