Question

A game involves rolling a fair six-sided dice. If the number obtained on the die is a multiple of three, the player wins an amount equal to the number on the dice times $20. If the number is not a multiple of three, the player gets nothing.

How will you model the simulation for the roll of a dice?
A. Use the numbers 1-20 to represent the numbers rolled when a player wins.
B. Use the numbers 1-6 to represent the unfavorable outcomes.
C. Use the numbers 1-3 to represent all the outcomes.
D. Use the numbers 1-10 to represent the unfavorable outcomes.
E. The problem cannot be solved using a simulation.

Answer 1

To simulate the dice game where the goal is to roll multiples of three, use the numbers 1-6 to represent the possible outcomes, assigning wins to rolls of 3 and 6.

Step-by-step explanation:

The question is about how to simulate the rolling of a dice in a game where the outcomes are multiples of three. The correct way to model the simulation for the roll of a dice would be option B: Use the numbers 1-6 to represent the unfavorable outcomes. This directly correlates the six faces of the dice with the potential outcomes. When simulating the roll, numbers 1 and 2 would be considered losses, 3 a win, 4 and 5 again losses, and 6 another win, with the wins obtaining a payout based on the number on the dice times $20.

If you were playing a simulation of the game, you could use a computer program or a random number generator set to produce numbers from 1 to 6 to represent each roll. The winning outcomes in this case would be when you roll a 3 or a 6, which are the multiples of three on the die. For each time a 3 or a 6 is rolled, the player would win $60 or $120, respectively. If any other number is obtained, the player would win nothing.