A game is said to be fair if the expected value (after considering the cost) is 0. This would mean that in the long run, both the player and the "house" or whoever is putting on the game, would expect to win nothing. If the value is positive, the game is in your favor. If the value is negative, the game is not in your favor. At a carnival, you pay $1 to choose a card from a standard deck. If you choose a red card you double your money, but if you pick a black card you do not get any. (A standard deck of cards has 52 card. 26 of the cards are red.) • E • •• • ••2 14444244 144 2 +t * + + +* • 2 • • • • 1. Complete the probability distribution below. P(x) Color of card x → Net Money Won or Lost Red + $ 24 Black Click to view hint 2. What is the expected value?

A game is said to be fair if the expected value (after considering the cost) is 0. This would mean that in the long run, both the player and the "house" or whoever is putting on the game, would expect to win nothing. If the value is positive, the game is in your favor. If the value is negative, the game is not in your favor. At a carnival, you pay $1 to choose a card from a standard deck. If you choose a red card you double your money, but if you pick a black card you do not get any. (A standard deck of cards has 52 card. 26 of the cards are red.) • E • •• • ••2 14444244 144 2 +t * + + +* • 2 • • • • 1. Complete the probability distribution below. P(x) Color of card x → Net Money Won or Lost Red + $ 24 Black Click to view hint 2. What is the expected value?

Name: Sta6.Fair Games and Expected Value: Game 1ngedstA game is said to be
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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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

100%

Sta
6.
Fair Games and Expected Value: Game 1
nged
st
A game is said to be fair if the expected value (after considering the cost) is 0. This would mean that in the long
run, both the player and the "house" or whoever is putting on the game, would expect to win nothing.
If the value is positive, the game is in your favor. If the value is negative, the game is not in your favor. At a
carnival, you pay $1 to choose a card from a standard deck. If you choose a red card you double your money,
but if you pick a black card you do not get any. (A standard deck of cards has 52 card. 26 of the cards are red.)
Exp
ut of
• • • • •2
Con
144 144 44 144 14
10
* * +* + +* t *
Less
• •:
Finish at
1. Complete the probability distribution below.
P(x)
Color of card x → Net Money Won or Lost
$4
Red
$4
Black
Click to view hint
2. What is the expected value?
u hint

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