Questions: A standard pair of six-sided dice is rolled. What is the probability of rolling a sum less than 11 ? Express your answer as a fraction or a decimal number rounded to four decimal places. Answer Tables How to enter your answer (opens in new window) Keyboard Shortcuts

Solution Steps

To find the probability of rolling a sum less than 11 with two six-sided dice, we need to determine the total number of possible outcomes and the number of favorable outcomes. The total number of outcomes when rolling two dice is 6 * 6 = 36. The favorable outcomes are those where the sum of the dice is less than 11. We will count these outcomes and then divide by the total number of outcomes to get the probability.

When rolling two six-sided dice, the total number of possible outcomes is given by: \[ \text{Total Outcomes} = 6 \times 6 = 36 \]

Next, we count the number of outcomes where the sum of the two dice is less than 11. The favorable outcomes are:

• Sums of 2 through 10 can be achieved with various combinations of the two dice. After counting, we find that there are 33 combinations that yield a sum less than 11.

The probability \( P \) of rolling a sum less than 11 is calculated as: \[ P(\text{sum} < 11) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{33}{36} \] This fraction can be simplified to: \[ P(\text{sum} < 11) = \frac{11}{12} \] To express this as a decimal rounded to four decimal places: \[ P(\text{sum} < 11) \approx 0.9167 \]

Final Answer