To determine the probability that the sum of two rolled dice is 4 or higher, we first need to know the total number of outcomes when rolling two six-sided dice. Since each die has 6 faces, the total number of outcomes is:
6 (for the first die) × 6 (for the second die) = 36 possible outcomes.
Next, we need to figure out how many of these outcomes yield a sum of 4 or more. To make this easier, let’s calculate the outcomes that do NOT meet this condition, which would be all the outcomes that result in a sum less than 4.
The sums that are less than 4 are:
- 2 (1 + 1)
- 3 (1 + 2, 2 + 1)
The outcomes for each of these sums are:
- For a sum of 2: 1 outcome (1,1)
- For a sum of 3: 2 outcomes (1,2) and (2,1)
This gives us a total of:
1 (for sum of 2) + 2 (for sum of 3) = 3 outcomes that are less than 4.
Now, subtracting the outcomes that do not meet the criterion from the total outcomes, we find the number of outcomes that yield a sum of 4 or higher:
36 (total outcomes) – 3 (outcomes less than 4) = 33 outcomes that are 4 or higher.
Finally, we calculate the probability:
Probability = Number of favorable outcomes / Total outcomes
Probability = 33 / 36 = 11 / 12.
Thus, the probability that the sum of the two dice rolls is 4 or higher is:
11/12 or approximately 0.9167.