Question

Caleb and Drew are playing a game with a pair of dice. Caleb needs a sum of 5 or greater to win. What is his probability of winning on his next turn?

Answer 1

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:

1. **Sum of 2:** (1, 1)
- Number of outcomes: 1

2. **Sum of 3:** (1, 2), (2, 1)
- Number of outcomes: 2

3. **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

\[
\boxed{\frac{5}{6}}
\]