10:16 < Back l 5G Discussion Details Intro Survey of Mathematics (23080.SEM) 4. You've entered the competition again but wore your contacts this time, bringing your vision up to a crisp 20/20. Your odds have changed drastically. The new probabilities of each outcome have changed, but neither the entry cost nor the dollar amount awarded have changed. You pay the $20 entry fee Hitting the target in the center wins you $5. You have a 4/8 probability of hitting the center Hitting the target in the second ring wins you $3. you have a 3/8 probability of hitting the second ring Hitting the target in the third ring wins you $1. You have a 1/8 probability of hitting the third ring Missing the target wins you $0. you have no chance of missing the target. What is the new expected value of the game? May the probabilities be ever in your favor.
10:16 < Back l 5G Discussion Details Intro Survey of Mathematics (23080.SEM) 4. You've entered the competition again but wore your contacts this time, bringing your vision up to a crisp 20/20. Your odds have changed drastically. The new probabilities of each outcome have changed, but neither the entry cost nor the dollar amount awarded have changed. You pay the $20 entry fee Hitting the target in the center wins you $5. You have a 4/8 probability of hitting the center Hitting the target in the second ring wins you $3. you have a 3/8 probability of hitting the second ring Hitting the target in the third ring wins you $1. You have a 1/8 probability of hitting the third ring Missing the target wins you $0. you have no chance of missing the target. What is the new expected value of the game? May the probabilities be ever in your favor.
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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You have entered an axe-throwing competition.
To enter the competition, you must pay a flat fee of $20.
Each contestant is allotted eight throws.
You left your glasses at home and thus are facing greater odds than would normally be expected from a talented athlete such as yourself.
Hitting the target in the center wins you $5. You have a 1/8 probability of hitting the center
Hitting the target in the second ring wins you $3. you have a 2/8 probability of hitting the second ring
Hitting the target in the third ring wins you $1. You have a 4/8 probability of hitting the third ring
Missing the target wins you $0. you have a 1/8 probability of missing the target.
Each throw is considered an event , so the following equation tells us the expected outcome per throw, which can be multiplied by 8 for the total expected outcome of the game.
E=-2.5(8/8)+5(1/8)+3(2/8)+1(4/8)+0(1/8)
E=-2.5+(5/8)+(3/4)+(1/2)+0
E=(-5/8)
E=-0.625
8E=-5
2. The expected value of the game is -$5
3. This is not a fair competition because you are expected to lose $5 each round you play due to your unaided nearsightedness.
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Discussion Details
Intro Survey of Mathematics (23080.SEM)
4. You've entered the competition again but
wore your contacts this time, bringing your
vision up to a crisp 20/20.
Your odds have changed drastically.
The new probabilities of each outcome have
changed, but neither the entry cost nor the
dollar amount awarded have changed.
You pay the $20 entry fee
Hitting the target in the center wins you $5.
You have a 4/8 probability of hitting the
center
Hitting the target in the second ring wins you
$3. you have a 3/8 probability of hitting the
second ring
Hitting the target in the third ring wins you
$1. You have a 1/8 probability of hitting the
third ring
Missing the target wins you $0. you have no
chance of missing the target.
What is the new expected value of the game?
May the probabilities be ever in your favor.
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