Two dice are rolled what are the odds of getting a smaller number on the second roll? P ( same number or sum greater than 8)
To find the odds of getting a smaller number on the second roll when two dice are rolled, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
First, let's analyze the possible outcomes for two dice rolls. Each die has six sides, numbered from 1 to 6. Therefore, the total number of possible outcomes when rolling two dice is 6 * 6 = 36.
Now, let's determine the number of favorable outcomes. We want to find the probability of getting a smaller number on the second roll, given that the first roll resulted in either the same number or a sum greater than 8.
1. If the first roll results in the same number (e.g., both dice show a 3), the only possible favorable outcome on the second roll is to get a number smaller than the number rolled in the first roll. Hence, there are 5 possible outcomes.
2. If the first roll results in a sum greater than 8, there are three combinations that satisfy this condition: (4, 5), (5, 4), and (6, 3). In each of these cases, the second roll can result in any number from 1 to the number rolled in the first roll. Therefore, there are 1 favorable outcome for (4, 5), 1 favorable outcome for (5, 4), and 2 favorable outcomes for (6, 3), giving a total of 4 outcomes.
Adding up the favorable outcomes, we have 5 + 4 = 9.
Therefore, the probability of getting a smaller number on the second roll, given that the first roll resulted in either the same number or a sum greater than 8, is 9 / 36.
Simplifying, we get 1 / 4 as the final answer, or 25% chance.