Two dice are rolled. Find the probability of the given outcome if the sum of the dots on the upward faces is less than 15.
since the maximum possible roll is 12,
P(<15) = 1
though I'm not sure what the "given outcome" is supposed to be ...
ss
Well, the sum of the dots on two dice can never be greater than 12, so I'm not sure how it could ever be less than 15. It's like trying to fit an elephant in a clown car – not really possible! The probability of the given outcome would basically be 0. But hey, at least we can have a good laugh about it, right? 🤡
To find the probability of an outcome when rolling two dice, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of outcomes when rolling two dice can be found by multiplying the number of outcomes for one die by the number of outcomes for the other. Since each die has 6 possible outcomes (1, 2, 3, 4, 5, or 6), the total number of outcomes for two dice is 6 * 6 = 36.
Now let's determine the number of favorable outcomes, i.e., the outcomes where the sum of the dots on the upward faces is less than 15.
To find all possible outcomes whose sum of dots on the upward faces is less than 15, we can list all the combinations where the sum is less than 15:
- (1, 1)
- (1, 2)
- (1, 3)
- ...
- (6, 5)
- (6, 6)
From the above list, we can see that there is a total of 36 favorable outcomes.
Therefore, the probability of the given outcome, where the sum of the dots on the upward faces is less than 15, is 36/36, which simplifies to 1.
In other words, the probability is 100% since all possible outcomes have a sum of dots less than 15 when rolling two dice.
To find the probability of the given outcome, we first need to determine the total number of possible outcomes when rolling two dice. Each die has six sides, so there are 6 possible outcomes for the first die and 6 possible outcomes for the second die. Therefore, the total number of possible outcomes is 6 x 6 = 36.
Now, let's find the number of outcomes where the sum of the dots on the upward faces is less than 15. Since the sum can be at most 12 (6 + 6), we don't need to consider outcomes where the sum is greater than or equal to 15.
To count the number of outcomes where the sum is less than 15, we can create a table of all possible combinations of the numbers on the dice:
| 1 | 2 | 3 | 4 | 5 | 6 |
--+---+---+---+---+---+---+
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
3 | 4 | 5 | 6 | 7 | 8 | 9 |
4 | 5 | 6 | 7 | 8 | 9 |10 |
5 | 6 | 7 | 8 | 9 |10 |11 |
6 | 7 | 8 | 9 |10 |11 |12 |
By examining the table, we can see that there are 36 - 6 = 30 outcomes where the sum is less than 15.
Finally, we can calculate the probability by dividing the number of successful outcomes (30) by the number of total possible outcomes (36). Therefore, the probability of the given outcome is 30/36 = 5/6, which can be further simplified if needed.