Questions: A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than 9 ? Express your answer as a fraction or a decimal number rounded to four decimal places.

$A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than 9 ? Express your answer as a fraction or a decimal number rounded to four decimal places.$

Transcript text: A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than 9 ? Express your answer as a fraction or a decimal number rounded to four decimal places.

Solution

Solution Steps

To solve this problem, we need to find the probability of rolling a sum greater than 9 with two six-sided dice. First, we will list all possible outcomes that result in a sum greater than 9, count these outcomes, and then divide by the total number of possible outcomes (which is 36, since each die has 6 faces).

Step 1: Total Outcomes

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

Step 2: Favorable Outcomes

Next, we identify the outcomes that result in a sum greater than 9. The pairs that yield such sums are:

(4, 6)
(5, 5)
(5, 6)
(6, 4)
(6, 5)
(6, 6)

Counting these pairs gives us: \[ \text{Favorable Outcomes} = 6 \]

Step 3: Probability Calculation

The probability $ P $ of rolling a sum greater than 9 is given by the ratio of favorable outcomes to total outcomes: \[ P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{6}{36} = \frac{1}{6} \approx 0.1667 \]