Answer the Bolded and underlined and do to the calculations for each one
Backgammon is a board game that was known to be prayed during the time of early Mesopotamia over five thousand years ago. The game involves two players with each of them having 15 checkers. These checkers shift between 24 triangles based on the two dice roll. Therefore, one wins when they have moved all their checkers (15 of them) to their own board and bear them off. One loses when their partner moves their checkers first.
The rules of the game are normally set and agreed in the international tournaments. For example, since the game is not played once but rather multiple times, the winner can be set as the person that achieves a certain target number of points first.
Some of the probability questions that I can ask in this game are;
- What are the odds of rolling a six as an addition of two dice?
- What is the probability of getting knocked off?
- What is the probability of getting at least one of the numbers in the range of 1 to 6 after rolling 2 dice?
- What are the odds of rolling doubles on the first roll?
Calculation 1
Calculate the probability of getting at least one of the numbers in the range of 1 to 6 after rolling two dice.
This is done through first determining the number of 36 possible outcomes that have at least a 2. Therefore: {1, 2} {2, 2}, {3, 2}, {4, 2}, {5, 2}, {6, 2}, {2, 1}, {2, 3}, {2, 4}, {2, 5}, {2, 6}. This shows that there are eleven ways that we can roll no less than one two using a 2 dice. The probability of rolling as a minimum 1 two with 2 dice is 11/36.
In this probability discussion, 2 has been used as the number of reference for purposes of the calculation since it’s in the range of 1 to 6.
Calculation 2
Using the addition rule, we can sum up different probabilities together. For instance, the probability of rolling at least one six from a 2 dice is eleven over thirty six (11/36), while that of rolling a six as an addition of 2 dice is five over thirty six (5/36). This then implies that the probability of rolling a six as an addition of 2 dice is calculated as 11/36 plus 5/36, which equals to 16/36.
0 comments