A fair six-sided die is rolled three times. What is the probability that exactly two of the rolls show a number greater than 4?

Mon, 04 May 2026 21:53:54 +0000

**Why Everyone’s Talking About the Probability of Rolling Two High Sixes on a Fair Die** Rolling a fair six-sided die three times is a familiar game for many—but what happens when you want exactly two rolls to show a number greater than 4? That’s a question sparking quiet curiosity across the US, where probability enthusiasts, educators, and casual learners alike are diving into structured chance. The scenario—A fair six-sided die is rolled three times. What is the probability that exactly two of the rolls show a number greater than 4?—reveals patterns in randomness that feel surprisingly relevant to daily decision-making. Whether you’re exploring chance in games, teaching math concepts, or analyzing random data, understanding this probability offers clarity in an unpredictable world. With mobile users seeking smart, reliable insights, this topic earns strong engagement and real search momentum. **The Real Math Behind Two “High” Rolls** The numbers on a fair die range from 1 to 6. Numbers greater than 4 are 5 and 6—two outcomes. So, the chance of rolling a number greater than 4 on a single roll is 2 out of 6, or one-third (1/3). Conversely, landing anywhere from 1 to 4 occurs with a 4/6 (2/3) probability. Since each roll is independent, we use basic probability to find the chance that exactly two rolls meet this higher threshold.