In a game of Catan, each turn two balanced die are rolled (each dice is six sided) and the numbers on the two die is added to determine the score (X) For example, if one dice shows 4 and
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.
In a game of Catan, each turn two balanced die are rolled (each dice is six sided) and the numbers on the two die is added to determine the score (X) For example, if one dice shows 4 and the other 3, then the score is 4+3=7. (The score in each turn is used to calculate how many resources each player gets).
1. How many unique values can X take?
2. Calculate the
3. Imagine you get 1 wheat resource every time the score is 1 or 6. What is the probability you get 1 wheat?
4. In a game of 50 turns, how many times do you expect to see a score of 7?
1)
When two fair dice are rolled.
The outcomes in a sample space is,
S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
Let x denote the score of sum of dice when two dies are rolled .
| Score(X) | number of outcomes |
| 2 | (1,1) |
| 3 | (1,2)(3,6) |
| 4 | (1,3)(2,2)(3,1) |
| 5 | (1,4)(2,3)(3,2)(4,1) |
| 6 | (1,5)(2,4)(3,3)(4,2)(5,1) |
| 7 | (1,6)(2,5)(3,4)(4,3)(5,2)(6,1) |
| 8 | (2,6)(3,5)(4,4)(5,3)(6,2) |
| 9 | (3,6)(4,5)(5,4)(6,3) |
| 10 | (4,6)(5,5)(6,4) |
| 11 | (5,6)(6,5) |
| 12 | (6,6) |
The number of unique values x can take is, 11.
That is, {2,3,4,5,6,7,8,9,10,11,12}
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