<p>To find the probability of rolling a sum of 4 or higher with two fair six-sided dice, we first need to determine the total number of possible outcomes when rolling the dice. Each die has 6 sides, so when you roll two dice, the total number of outcomes is:</p>
<p> <strong>Total outcomes:</strong> 6 (from the first die) x 6 (from the second die) = 36.</p>
<p>Next, we need to count the number of favorable outcomes that result in a sum of 4 or greater. The possible sums from two dice can range from 2 (1+1) to 12 (6+6). To find the sums less than 4, we can list them:</p>
<p> <strong>Sums less than 4:</strong>
– A sum of 2: (1,1) — 1 outcome
– A sum of 3: (1,2), (2,1) — 2 outcomes
– **Total outcomes for sums less than 4**: 1 + 2 = 3 outcomes</p>
<p>Since there are a total of 36 outcomes, the number of outcomes that result in a sum of 4 or higher is the total outcomes minus those that are less than 4:</p>
<p> <strong>Favorable outcomes for sums of 4 or higher:</strong> 36 (total outcomes) – 3 (outcomes for sums less than 4) = 33 outcomes</p>
<p>Finally, the probability is given by the ratio of the number of favorable outcomes to the total outcomes. Thus, the probability of rolling a sum of 4 or higher is:</p>
<p> <strong>Probability = Favorable Outcomes / Total Outcomes = 33 / 36 = 11/12</strong>
<p>In conclusion, the probability of rolling a sum of 4 or higher when using two fair six-sided dice is <strong>11/12 or approximately 0.917</strong>, which means you have a high chance of rolling a sum that is 4 or greater!</p>