A game is played by rolling the two dice, three times (toss the two dice three times). What is the probability of getting a number larger than 9 for the first time on the third roll? Show and explain your work and give your answer as a fraction in lowest terms.
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.
A game is played by rolling the two dice, three times (toss the two dice three times).
What is the probability of getting a number larger than 9 for the first time on the third roll? Show and explain your work and give your answer as a fraction in lowest terms.
It is given that there are two dice that are thrown three times.
Consider that D1 and D2 are defined as the two dice. Thus, the possible number of sum for both dice. Thus,
D1/D2 |
1 |
2 |
3 |
4 |
5 |
6 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
Thus, the probability that the dice sum (number) is larger than 9, can be calculated as:
Assume that X is defined as the event when the sum of both dice( a number) is larger than 9. Thus,
Thus,
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