Two dice are rolled. Find the odds that the score on the dice is either 10 or at most 5
how many ways to get 10 ?
how many ways to get at most 5 ?
add them up
find prob of that = ?/36
proceed as I showed you in previous post
To find the odds of the score on the two dice being either 10 or at most 5, we need to determine the number of favorable outcomes and divide it by the total number of outcomes.
Let's break down the favorable outcomes for each scenario:
1. The score on the dice is 10:
The only possible combination that gives a sum of 10 is (4, 6) and its mirror (6, 4). So, there are 2 favorable outcomes for this scenario.
2. The score on the dice is at most 5:
We can count the favorable outcomes for scores less than or equal to 5:
- For a sum of 2, there is only one combination: (1, 1).
- For a sum of 3, we have two combinations: (1, 2) and (2, 1).
- For a sum of 4, there are three combinations: (1, 3), (2, 2), and (3, 1).
- For a sum of 5, we have four combinations: (1, 4), (2, 3), (3, 2), and (4, 1).
Adding up the favorable outcomes for the second scenario gives us a total of 1 + 2 + 3 + 4 = 10.
Now, let's calculate the total number of outcomes:
Since two dice are rolled simultaneously, each die can have 6 possible outcomes. Thus, the total number of outcomes is 6 * 6 = 36.
Finally, we can find the odds by dividing the number of favorable outcomes by the total number of outcomes:
Odds = (Number of Favorable Outcomes) / (Total Number of Outcomes)
= (2 + 10) / 36
= 12 / 36
= 1 / 3
Therefore, the odds that the score on the two dice is either 10 or at most 5 is 1/3.
To find the odds that the score on two dice is either 10 or at most 5, we first need to determine the possible outcomes for each condition separately and then calculate the total number of favorable outcomes.
1. Finding the number of favorable outcomes for a score of 10:
- The possible outcomes for rolling two dice are {1,1}, {1,2}, {1,3}, ..., {6,6}.
- We need to find the combinations of numbers that sum up to 10.
- Here are the possible combinations: {4,6}, {5,5}, {6,4}.
- Therefore, there are 3 favorable outcomes for a score of 10.
2. Finding the number of favorable outcomes for a score at most 5:
- We need to consider the combinations of numbers that sum up to a value less than or equal to 5.
- The combinations are: {1,1}, {1,2}, {2,1}, {1,3}, {3,1}, {2,2}, {1,4}, {4,1}, {3,2}, {2,3}.
- Therefore, there are 10 favorable outcomes for a score at most 5.
Now, let's calculate the total number of possible outcomes when rolling two dice:
- Since each die has 6 possible outcomes (1, 2, 3, 4, 5, 6), the total number of outcomes for two dice is 6 * 6 = 36.
Finally, to find the odds, we divide the number of favorable outcomes by the total number of possible outcomes:
- Odds = (Number of favorable outcomes) / (Total number of outcomes)
- Odds = (3 + 10) / 36
- Odds = 13 / 36
Therefore, the odds that the score on two dice is either 10 or at most 5 is 13/36.