Question

consider rolling dice and getting a total of 8 which is more likely: rolling a total of 8 when two dice are rolled or rolling a total of 8 when three dice are rolled?

Answer 1

The probability of rolling a total of 8 is higher when two dice are rolled compared to when three dice are rolled.

Step-by-step explanation:

The probability of rolling a total of 8 when two dice are rolled can be calculated by counting the number of combinations that add up to 8. There are 5 ways to roll a total of 8: (2,6), (3,5), (4,4), (5,3), (6,2). Since there are 36 equally likely outcomes when rolling two dice, the probability is 5/36.

The probability of rolling a total of 8 when three dice are rolled can be calculated in a similar way. There are 10 ways to roll a total of 8: (2,3,3), (2,4,2), (2,2,4), (3,2,3), (3,3,2), (4,2,2), (2,5,1), (5,2,1), (1,5,2), (1,2,5). Since there are 216 equally likely outcomes when rolling three dice, the probability is 10/216.

Therefore, the probability of rolling a total of 8 is higher when two dice are rolled compared to when three dice are rolled.

Answer 2

It is more likely to roll a total of 8 with two dice than with three dice. The probability with two dice is 5/36, which is higher compared to the probability with three dice where the distribution becomes wider and outcomes near the middle are more likely.

Step-by-step explanation:

The probability of rolling a total of 8 with two dice is different from rolling a total of 8 with three dice. To find the probability with two dice, we need to consider all the possible combinations that add up to 8: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). There are 6 x 6 = 36 possible outcomes when rolling two dice, and there are 5 favorable outcomes for getting a sum of 8. Hence, the probability is 5/36.

With three dice, there are a total of 6 x 6 x 6 = 216 possible outcomes. Computing the exact number of combinations that sum up to 8 is more complex because there are more variables. However, it's important to note that when adding an additional die, the probability distribution becomes wider and flatter. This means outcomes near the middle numbers (like 10.5, which is the average roll of three dice) become more likely, and outcomes further away from the middle, like 8, become less likely compared to rolling two dice.

Therefore, it is more likely to roll a total of 8 when two dice are rolled than when three dice are rolled. This conclusion is consistent with the principles of probability distribution and combinatorial calculations.