To determine the probability that Caleb wins by rolling a sum of 5 or greater with a pair of dice, we first need to calculate the total number of possible outcomes when rolling two dice.
When rolling two six-sided dice, there are a total of \(6 \times 6 = 36\) possible outcomes.
Next, we need to find the outcomes that give a sum of 5 or more. We'll first count the outcomes that result in sums less than 5:
- A sum of 2: (1,1) → 1 outcome
- A sum of 3: (1,2), (2,1) → 2 outcomes
- A sum of 4: (1,3), (2,2), (3,1) → 3 outcomes
Now we can add these outcomes together:
- Total outcomes for sums less than 5 = 1 + 2 + 3 = 6 outcomes.
Now we can find the outcomes for sums of 5 or greater:
- Total outcomes for sums of 5 or more = Total outcomes - outcomes with sums less than 5 = 36 - 6 = 30 outcomes.
Finally, to find the probability of Caleb winning (i.e., rolling a sum of 5 or greater), we take the number of favorable outcomes and divide by the total number of outcomes:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{30}{36} = \frac{5}{6} \approx 0.83. \]
Therefore, the probability that Caleb wins on his next turn is 0.83.