Two dice are rolled and someone indicates that the two numbers that come up are different. Find the probability that the sum of the two numbers is 4.
To find the probability that the sum of the two numbers is 4, we need to count the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the total number of possible outcomes when rolling two dice. Each die has 6 possible outcomes, so the total number of outcomes is 6 x 6 = 36.
Now, let's consider the different ways we can get a sum of 4 using two dice:
1. We can roll a 1 on the first die and a 3 on the second die.
2. We can roll a 2 on the first die and a 2 on the second die.
3. We can roll a 3 on the first die and a 1 on the second die.
This makes a total of 3 favorable outcomes.
Therefore, the probability of getting a sum of 4, given that the two numbers rolled are different, is 3/36.
Simplifying, this is equal to 1/12. So, the probability is 1 in 12 or approximately 0.0833.
To find the probability that the sum of the two numbers is 4, we first need to determine the sample space—i.e., all possible outcomes when two dice are rolled. Each die has 6 possible outcomes (numbers 1 through 6), so the total number of outcomes when two dice are rolled is 6^2 = 36.
Next, we need to determine the number of favorable outcomes—i.e., the number of outcomes where the two numbers are different and the sum is 4. We can list all possible combinations of numbers that have a sum of 4: {(1, 3), (2, 2), (3, 1)}.
Out of these three combinations, only one has two different numbers—(1, 3). The other two combinations—(2, 2) and (3, 1)—have the same number on both dice.
Therefore, the number of favorable outcomes is 1.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes = 1 / 36.
Therefore, the probability that the sum of the two numbers is 4, given that the two numbers are different, is 1/36.
36 total possibilities. 4 can be obtained by 3,1 or 1,3 or 2,2.
3/36 = ?