Tyler is playing a game of chance in which four cards are drawn from a standard deck of 52 cards. Tyler guesses the suit of each card before it is drawn. The cards are replaced in the deck after each draw. Tyler pays $1 to play. If Tyler guesses the right suit every time, he gets his money back and $162. Complete the probability distribution table. Probability Distribution Table P(x) -1 What is your long-term expected profit per game? %$4 What is the standard deviation? $4
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.
Let X be a random variable such that
X: Payoff of guessing the suit of the card
Assuming that each suit is equally likely to be drawn and guessed,
| X | P(x) |
| -1 | 0.25 |
| 162 | 0.75 |
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