Q 51. Coin Game: You and your two friends play the following coin game: You each flip a fair dime once - tails) different from the other two people, that erson pays the others $1 each. If all three of you get the same outcome, no one wins or loses any money. Let W be your winnings (in $) from this game. if one person gets an outcome (heads or a) Find the probability mass function for W and display in table form. Show your work and justify. Hint: first, write out the sample space. b) Find the mean of W and interpret your answwer in terms of the game. Show your calculations and then circle your final answer. c) Now, you and your friends roll a fair die. Then you play the above coin tossing game. If the die shows an odd umber, then the person who gets an outcome (heads or tails) different from the other two people will pay each of the others $1. If the die shows an even number, then the person who gets an outcome (heads or tails) different from the other two people will pay each of the others $2. If all three of you get the same outcome, no one wins or loses any money. Suppose you do not win or lose anything from this game. WVhat is the probability that the die showed an even number? Show your work, name any theorems/methods you use, and then circle your final answer.

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A:

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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.