You are going to roll two dice. Let the variable x = the sum of the numbers rolled.
What is the probability that x = 9?
Of the 36 possible results of a throw of two dice, 4 add up to nine. They are 3+6, 4+5, 5+4 and 6+3.
So the probabability of throwing a nine is 4/36 = 1/9
To find the probability that the sum of the numbers rolled is 9, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Determine the favorable outcomes.
The possible outcomes for rolling two dice can be represented by a sample space, which consists of all possible pairs of numbers that can be rolled.
We can list all the possible outcomes where the sum of the numbers rolled is 9:
(3, 6), (4, 5), (5, 4), (6, 3)
Therefore, there are 4 favorable outcomes.
Step 2: Determine the total number of possible outcomes.
When rolling two dice, each die can have 6 possible outcomes, resulting in a total of 6 x 6 = 36 possible outcomes.
Step 3: Calculate the probability that x = 9.
We divide the number of favorable outcomes (4) by the total number of possible outcomes (36):
Probability = Favorable outcomes / Total outcomes
Probability = 4 / 36
Probability = 1 / 9
Therefore, the probability that the sum of the numbers rolled is 9 is 1/9.
To find the probability that the sum of the two dice is 9, we need to determine the number of favorable outcomes (the sum is 9) and the total number of possible outcomes.
There are 36 possible outcomes when rolling two dice because each die has 6 possible outcomes (1, 2, 3, 4, 5, or 6), so the total possible outcomes for two dice is 6 * 6 = 36.
To find the favorable outcomes, we need to determine all the ways the dice can sum up to 9:
1. Rolling a 3 on the first die and a 6 on the second die: There is only one way to get a sum of 9 in this case.
2. Rolling a 4 on the first die and a 5 on the second die: Again, there is only one way to get a sum of 9 in this case.
3. Rolling a 5 on the first die and a 4 on the second die: This is the same as the previous case, so it is also one favorable outcome.
4. Rolling a 6 on the first die and a 3 on the second die: Same as the first case, so one favorable outcome.
In total, we have four favorable outcomes.
Therefore, the probability that the sum of the two dice is 9 is 4 favorable outcomes out of 36 possible outcomes, which simplifies to 4/36 or 1/9.