To find Caleb's probability of winning on his next turn by rolling a sum of 5 or greater with two dice, we first determine the total number of possible outcomes when rolling two dice.
Each die has 6 faces, so when rolling two dice, the total number of outcomes is:
\[ 6 \times 6 = 36 \]
Next, we need to figure out how many of these outcomes result in a sum of 5 or greater. We can do this by counting the total outcomes that result in sums less than 5 and then subtracting from the total possible outcomes.
The sums that are less than 5 are: 2, 3, and 4. We can calculate the number of ways to achieve each of these sums:
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Sum of 2: (1, 1)
- Number of outcomes: 1
-
Sum of 3: (1, 2), (2, 1)
- Number of outcomes: 2
-
Sum of 4: (1, 3), (2, 2), (3, 1)
- Number of outcomes: 3
Now we sum the outcomes for sums less than 5:
\[ 1 \text{ (for 2)} + 2 \text{ (for 3)} + 3 \text{ (for 4)} = 6 \]
Thus, the number of outcomes that result in a sum of 5 or greater is:
\[ 36 - 6 = 30 \]
Finally, to find the probability of winning (summing 5 or greater), we divide the number of favorable outcomes by the total number of outcomes:
\[ \text{Probability of winning} = \frac{\text{Number of outcomes with sum} \geq 5}{\text{Total outcomes}} = \frac{30}{36} = \frac{5}{6} \]
Thus, Caleb's probability of winning on his next turn is
\[ \boxed{\frac{5}{6}} \]