If two fair dice are rolled, find the probability that the sum of the dice is 6, given that the sum is greater than 3.
0.151
Well, when it comes to fair dice, sometimes the odds are stacked against us. But let's see if we can roll with it and find the probability!
When the sum of two fair dice is greater than 3, we can eliminate a few possibilities. We know that rolling a sum of 2 is not possible, since each die has a minimum value of 1. So, our possible sums are 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Out of these possibilities, we want to find the probability that the sum is 6. There are a few ways to achieve this sum: (1, 5), (2, 4), and (3, 3). That's a total of 3 favorable outcomes.
Since we're assuming the sum is greater than 3, we need to consider the remaining possibilities: 4, 5, 6, 7, 8, 9, 10, 11, and 12. There are a total of 9 possible outcomes.
So, the probability of rolling a sum of 6, given that the sum is greater than 3, would be 3/9, which simplifies to 1/3.
Remember, though, in the world of dice, probability can be a bit of a roll of the dice. But with a little humor and some calculation, we can try to find our way through!
To find the probability that the sum of two fair dice is 6, given that the sum is greater than 3, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Total Number of Outcomes:
When two dice are rolled, each die has 6 possible outcomes (from 1 to 6). Therefore, the total number of outcomes is 6*6 = 36.
Favorable Outcomes:
To find the favorable outcomes, we need to consider the combinations of the two dice that give a sum of 6 but are also greater than 3. The following combinations satisfy this condition:
(1, 5) - 1st die shows a 1, and the 2nd die shows a 5.
(2, 4) - 1st die shows a 2, and the 2nd die shows a 4.
(3, 3) - 1st die shows a 3, and the 2nd die shows a 3.
(4, 2) - 1st die shows a 4, and the 2nd die shows a 2.
(5, 1) - 1st die shows a 5, and the 2nd die shows a 1.
So, there are 5 favorable outcomes.
Probability Calculation:
The probability of an event is given by the ratio of favorable outcomes to total outcomes. Therefore, the probability that the sum of two fair dice is 6, given that the sum is greater than 3, is:
P(Sum of 6 | Sum > 3) = Favorable Outcomes / Total Outcomes
= 5 / 36
Therefore, the probability is 5/36.
To find the probability that the sum of two dice is 6, given that the sum is greater than 3, we will first determine the total number of possible outcomes for rolling two dice. Then, we will calculate the number of those outcomes where the sum is greater than 3 and the sum is equal to 6. Finally, we will divide the number of favorable outcomes by the total number of possible outcomes.
Step 1: Determine the total number of possible outcomes for rolling two dice.
Each die has six sides, so the total number of outcomes for one die is 6. Since we are rolling two dice, the total number of possible outcomes is 6 multiplied by 6, which is 36.
Step 2: Calculate the number of outcomes where the sum is greater than 3 and the sum is equal to 6.
To have a sum greater than 3, we can obtain one of the following outcomes: {4, 2}, {5, 1}, {6, 1}. Out of these three outcomes, only one outcome has a sum equal to 6, which is {4, 2}. Therefore, the number of outcomes where the sum is greater than 3 and the sum is 6 is 1.
Step 3: Divide the number of favorable outcomes by the total number of possible outcomes.
We have one favorable outcome and 36 possible outcomes. Therefore, the probability that the sum of two fair dice is 6, given that the sum is greater than 3, is 1/36.
So, the probability is 1/36.
You have to make table of the sample space
1,1 1,2 1,3 ... 1,6
2,1...............2,6
3,1................3,6
4,1
5,1
6,1
You should have 36 entries.
Given the sum is greater than 3 will eliminate 1,1 1,2 and 2,1
So you are working with 33 possibilities for the denominator
The numerator will be the number of times you find 6 as the sum in your table.