Objective: Construct a probability distribution and use it to find the expected value of the game. Introduction: Here's the game: there are two boxes with four balls each. To play, you put on a blindfold and then pick one ball at random from each box.

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter14: Counting And Probability
Section14.FOM: Focus On Modeling: The Monte Carlo Method
Problem 3P: Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if...
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A game of chance and the expected value
Objective: Construct a probability distribution and use it to find the expected value of the game.
Introduction: Here's the game: there are two boxes with four balls each. To play, you put on a
blindfold and then pick one ball at random from each box.
There are two red, one blue and one green ball in the box on the left. There are two blue, one red
and one green ball in the box on the right.
Payouts:
$0 if the balls are different colors,
$0.50 if they are both red,
$1 if they are both blue, and
$16 if they are both green.
Question:
If the game costs $1 to play, would you expect to gain or lose money on average? And how
much?
In your solution, you must show:
How you compute the probability that payout is $0.
How you compute the probability that payout is $0.50.
How you compute the probability that payout is $1.
How you compute the probability that payout is $16.
Summarize the data into a probability table.
Compute the expected value.
Remember to account for the $1 you pay to play the game.
Your conclusion.
Transcribed Image Text:A game of chance and the expected value Objective: Construct a probability distribution and use it to find the expected value of the game. Introduction: Here's the game: there are two boxes with four balls each. To play, you put on a blindfold and then pick one ball at random from each box. There are two red, one blue and one green ball in the box on the left. There are two blue, one red and one green ball in the box on the right. Payouts: $0 if the balls are different colors, $0.50 if they are both red, $1 if they are both blue, and $16 if they are both green. Question: If the game costs $1 to play, would you expect to gain or lose money on average? And how much? In your solution, you must show: How you compute the probability that payout is $0. How you compute the probability that payout is $0.50. How you compute the probability that payout is $1. How you compute the probability that payout is $16. Summarize the data into a probability table. Compute the expected value. Remember to account for the $1 you pay to play the game. Your conclusion.
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