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?

1 answer

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

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