GED Math: Probability of Rolling a Sum of 9 with Two Dice

Understanding Dice Probabilities

• 🎲 The problem involves finding the probability of rolling a sum of 9 when a pair of dice is tossed.
• 🎯 To solve this, a table is created to visualize all possible outcomes.

Constructing the Outcome Table

• 📊 The first die can show numbers 1 through 6, and the second die also shows numbers 1 through 6.
• ➕ The table displays the sum of the two dice for each combination.
• 🔢 The total number of possible outcomes is calculated as 6 (outcomes for the first die) multiplied by 6 (outcomes for the second die), resulting in 36 total sum values.

Identifying Successful Events

• 🔍 The goal is to find the number of ways to achieve a sum of 9.
• 🔢 The combinations that result in a sum of 9 are: (6, 3), (5, 4), (4, 5), and (3, 6).
• ✅ There are four successful events where the sum is 9.

Calculating the Probability

• ➗ Probability is defined as the ratio of successful events to the total possible outcomes.
• 🔢 The probability of rolling a sum of 9 is 4 successful events out of 36 total outcomes, or 4/36.
• ➗ Simplifying the fraction 4/36 by dividing both the numerator and denominator by 4 results in 1/9.