Probability Distribution of Dice Game

The video tutorial explains a board game where players roll two three-sided dice and calculate the non-negative difference between the numbers shown. It guides viewers through constructing the theoretical probability distribution of the difference, denoted as 'd'. The tutorial includes a detailed analysis of all possible dice roll scenarios and calculates the probability for each possible difference outcome, resulting in a complete probability distribution for the game.

What is the main objective of the board game described in the video?

• To roll the highest number possible

• To achieve a specific sum with the dice

• To calculate the non-negative difference between two dice

• To match the numbers on both dice

What is the first step in constructing the theoretical probability distribution of the difference?

• Identifying all possible outcomes of the dice rolls

• Calculating the sum of the dice

• Ignoring the lower number on the dice

• Rolling the dice multiple times

How many possible outcomes are there when rolling two three-sided dice?

• 9

• 6

• 15

• 12

What is the probability of getting a difference of 0?

• 1/2

• 1/3

• 2/9

• 1/9

How many scenarios result in a difference of 1?

• 2

• 3

• 4

• 5

What is the probability of obtaining a difference of 2?

• 4/9

• 1/9

• 2/9

• 1/3

Which of the following is NOT a possible difference when rolling two three-sided dice?

• 2

• 0

• 1

• 3

What is the total probability of all possible differences combined?

• 4/9

• 2

• 1

• 1/3

How is the non-negative difference calculated in the game?

• By subtracting the smaller number from the larger one

• By adding the numbers on the dice

• By multiplying the numbers on the dice

• By dividing the larger number by the smaller one

What is the significance of constructing the theoretical probability distribution in this game?

• To predict the most common outcome

• To determine the winner of the game

• To understand the likelihood of each possible difference

• To calculate the average roll