You draw two cards from a deck and win the following: $200 if you draw any pair $50 if you draw two cards of the same suit $0 if you draw anything else a) What is your expected winnings? b) Now assume you are required to pay a $30 fee to play. Should you play? Why?
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.
2. You draw two cards from a deck and win the following:
- $200 if you draw any pair
- $50 if you draw two cards of the same suit
- $0 if you draw anything else
a) What is your expected winnings?
b) Now assume you are required to pay a $30 fee to play. Should you play? Why?
There are 13 denominations. We can pick a denomination for the pair in 13 ways.
When the denomination is picked then there are 4 cards of the same denomination.
We can pick any 2 cards from them in 4C2=6 ways
So total number of ways to pick any pair is=
There are 4 suits. We can pick a suit in 4 ways. In a suit, there are 13 cards. We can pick 2 cards from 13 cards in 13C2=78 ways
So the total number of ways to pick two cards of the same suit is=
We can draw any 2 cards from 52 cards in 52C2=326 ways
So there are (326-78-312)=936 ways to get other.
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