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?
Responses

0.67
0.67

0.17
0.17

0.83
0.83

0.40
0.40

Answer 1

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**.