Question

The goal of playing a dice game is to roll a 4 or higher. You have the option to roll one 8-sided die, using the one result, or roll two 4-sided dice, adding the results. Which option gives you a higher probability of rolling a 4 or better?

Answer 1

When compared, rolling two 4-sided dice has a higher probability (11/16) of achieving a sum of 4 or better compared to rolling one 8-sided die, which has a lower probability of 5/8.

Step-by-step explanation:

To determine which option gives a higher probability of rolling a 4 or better, we need to analyze the outcomes of both the 8-sided die and the two 4-sided dice.

For the 8-sided die (with faces numbered 1 to 8), there are 5 outcomes (4, 5, 6, 7, 8) that result in a 4 or higher. Since there are 8 possible outcomes in total, the probability of rolling a 4 or better with one roll of an 8-sided die is 5/8.

For the two 4-sided dice (each with faces numbered 1 to 4), the smallest combined outcome is 2 (1+1) and the largest is 8 (4+4). To roll a sum of 4 or higher is possible with the following combinations:

• 2+2
• 2+3, 3+2
• 2+4, 4+2, 3+3
• 3+4, 4+3
• 4+4

There are 11 combinations that yield a 4 or better out of 16 total combinations (since each die has 4 sides, and we roll two dice, there are 4 * 4 = 16 combinations). So, the probability of rolling a 4 or better with two 4-sided dice is 11/16.

Comparing these probabilities, we can see that the probability of rolling a 4 or better with two 4-sided dice (11/16) is higher than the probability of rolling a 4 or better with one 8-sided die (5/8).