A person must pay $4 to play a certain game at the casino. Each player has a probability of 0.21 of winning $14, for a net gain of $10 (the net gain is the amount won 14 minus the cost of playing 4). Each player has a probability of 0.79 of losing the game, for a net loss of $4 (the net loss is simply the cost of playing since nothing else is lost). What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places. Expected Value = $ If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind? O ahead O behind

College Algebra
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ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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A person must pay $4 to play a certain game at the casino. Each player has a probability of 0.21 of
winning $14, for a net gain of $10 (the net gain is the amount won 14 minus the cost of playing 4).
Each player has a probability of 0.79 of losing the game, for a net loss of $4 (the net loss is simply
the cost of playing since nothing else is lost).
What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the
Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with
two decimal places.
Expected Value = $
%3D
If a person plays this game a very large number of times over the years, do we expect him/her to
come out financially ahead or behind?
O ahead
O behind
Transcribed Image Text:A person must pay $4 to play a certain game at the casino. Each player has a probability of 0.21 of winning $14, for a net gain of $10 (the net gain is the amount won 14 minus the cost of playing 4). Each player has a probability of 0.79 of losing the game, for a net loss of $4 (the net loss is simply the cost of playing since nothing else is lost). What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places. Expected Value = $ %3D If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind? O ahead O behind
Expert Solution
Step 1

Let, X = Net gain or loss after playing a game. Then;

X=10, with probability 0.21-4, with probability 0.79

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