To find the probability of rolling a sum of 5 or lower with two six-sided dice, we first need to determine the total possible outcomes when rolling the two dice. Each die has 6 sides, so when rolling two dice, the total combinations are:
Total Outcomes = 6 (sides on die 1) × 6 (sides on die 2) = 36.
Next, we will count the number of outcomes that result in a sum of 5 or less. Let’s look at the possibilities:
- Sum of 2: (1,1)
- Sum of 3: (1,2), (2,1)
- Sum of 4: (1,3), (2,2), (3,1)
- Sum of 5: (1,4), (2,3), (3,2), (4,1)
If we count them:
- 1 outcome for a sum of 2
- 2 outcomes for a sum of 3
- 3 outcomes for a sum of 4
- 4 outcomes for a sum of 5
This gives us a total of:
Total Favorable Outcomes = 1 + 2 + 3 + 4 = 10.
Now, we can use the formula for probability:
Probability = (Number of Favorable Outcomes) / (Total Outcomes)
Substituting the values we found:
Probability = 10 / 36 = 5 / 18.
Thus, the probability that the sum of the two dice is 5 or lower is 5/18.