D die is rolled twice, what is the probability that the sum of the num...
Sample space = { (1,4) , (4,1) , (2,3) , (3,2) }
Total possibilities = 6*6 = 36
Probability = 4/36 = 1/9
D die is rolled twice, what is the probability that the sum of the num...
**Solution:**
To find the probability of getting a sum of 5 when rolling a die twice, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
**Total number of possible outcomes:**
When rolling a die twice, there are 6 possible outcomes for each roll. Since each roll is independent, the total number of possible outcomes is the product of the number of outcomes for each roll, which is 6 * 6 = 36.
**Number of favorable outcomes:**
We need to determine the number of ways to get a sum of 5 when rolling a die twice. Let's consider all the possible combinations:
- (1, 4)
- (2, 3)
- (3, 2)
- (4, 1)
There are 4 possible combinations that result in a sum of 5.
**Calculating the probability:**
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, the probability of getting a sum of 5 is 4/36, which simplifies to 1/9.
Therefore, the correct answer is option A) 1/9.