## Summary

- • The probability of rolling a 2 on a fair six-sided dice is 1/6.
- • The expected value of rolling a single fair six-sided dice is 3.5.
- • The maximum possible sum of two six-sided dice rolls is 12.
- • The probability of rolling a double on two fair six-sided dice is 1/6.
- • The probability of rolling a 7 on two fair six-sided dice is 1/6.
- • The probability of rolling a total greater than 9 on two fair six-sided dice is 5/12.
- • The probability of rolling a 6 when throwing a fair six-sided dice is 1/6.
- • The probability of rolling an odd number on a fair six-sided dice is 1/2.
- • The probability of rolling a prime number on a fair six-sided dice is 1/2.
- • The probability of rolling a 5 or 6 on a fair six-sided dice is 1/3.
- • The probability of rolling a 3 or 4 on a fair six-sided dice is 1/3.
- • The probability of rolling a 2, 3, or 4 on a fair six-sided dice is 1/2.
- • The probability of rolling a 1 or 6 on a fair six-sided dice is 1/3.
- • The probability of rolling a 5 on a fair six-sided dice is 1/6.
- • The probability of rolling a 2 or 5 on a fair six-sided dice is 1/3.

Rolling the dice – a game of chance, probability, and infinite possibilities. From the thrill of landing on that coveted double to the reassurance that half the numbers are prime, each roll is a mathematical dance of fate. With a 1/6 chance of hitting that elusive 2 or a 5/12 shot at scoring greater than 9, every toss brings a new twist to the table. So, brace yourself for a rollercoaster ride through the world of dice probabilities; after all, its not just about luck – its about knowing the odds and playing them right.

## Expected value of rolling a single fair six-sided die

- The expected value of rolling a single fair six-sided dice is 3.5.

### Interpretation

The expected value of rolling a single fair six-sided dice is like the ultimate game of chance with a hint of predictability—kind of like trying to navigate through rush hour traffic with a Magic 8-Ball. While we may never know if we'll hit a lucky streak and roll a six, or end up with a dreaded one, statistically speaking, our best bet is to hedge our bets on a nice, safe 3.5. It's the jackpot of mediocrity we can all strive for in the unpredictable dance of dice and destiny.

## Maximum possible sum of two six-sided dice

- The maximum possible sum of two six-sided dice rolls is 12.

### Interpretation

In the high-stakes world of dice rolls, where luck can either make you a hero or reduce you to a mere mortal, the maximum possible sum of 12 serves as a tantalizingly close yet unattainable pinnacle of fortune. Much like chasing the elusive pot of gold at the end of a rainbow, rolling two six-sided dice and landing on a sum of 12 represents the ultimate quest for glory—a daring feat that few dare to dream of achieving. So, as we take a chance on the roll of the dice, let us remember that in the game of life, sometimes coming close to greatness is an accomplishment in itself.

## Probability of rolling specific combinations on two fair six-sided dice

- The probability of rolling a double on two fair six-sided dice is 1/6.
- The probability of rolling the same number on two fair six-sided dice is 1/6.
- The probability of rolling a double 6 on two fair six-sided dice is 1/36.

### Interpretation

In the unpredictable world of dice rolls, the odds of landing on a double or matching numbers may seem like a game of chance. With a 1/6 chance of rolling a double or the same number, it's as if Lady Luck is sending a subtle reminder that symmetry isn't always a coincidence. But aiming for that elusive double 6? Well, that's where the true test of fate lies, with a mere 1/36 chance of hitting the jackpot. So, next time you feel like rolling the dice, just remember to keep your expectations high and your probabilities even higher.

## Probability of rolling specific sums on two fair six-sided dice

- The probability of rolling a 7 on two fair six-sided dice is 1/6.
- The probability of rolling a total greater than 9 on two fair six-sided dice is 5/12.
- The probability of rolling a total of 4 on two fair six-sided dice is 1/12.
- The probability of rolling a sum of 7 or 11 on two fair six-sided dice is 1/6.
- The probability of rolling a 10 on two fair six-sided dice is 1/12.
- The probability of rolling a number greater than 9 on two fair six-sided dice is 7/12.
- The probability of rolling a sum of 8 on two fair six-sided dice is 5/36.
- The probability of rolling a sum of 9 on two fair six-sided dice is 4/36.
- The probability of rolling a sum of 10 on two fair six-sided dice is 3/36.
- The probability of rolling a sum of 11 on two fair six-sided dice is 2/36.
- The probability of rolling a sum of 12 on two fair six-sided dice is 1/36.
- The probability of rolling a sum of 4 on two fair six-sided dice is 3/36.
- The probability of rolling a sum of 5 on two fair six-sided dice is 4/36.
- The probability of rolling a sum of 2 on two fair six-sided dice is 1/36.
- The probability of rolling a sum of 3 on two fair six-sided dice is 2/36.
- The probability of rolling a sum of 6 on two fair six-sided dice is 5/36.
- The probability of rolling a sum of 12 on two fair six-sided dice is 1/36.
- The probability of rolling a sum of 3 or 4 on two fair six-sided dice is 1/12.
- The probability of rolling a sum of 5 or 6 on two fair six-sided dice is 1/9.
- The probability of rolling a sum of 7 or 8 on two fair six-sided dice is 1/6.
- The probability of rolling a sum of 9 on two fair six-sided dice is 5/36.
- The probability of rolling a sum of 10 on two fair six-sided dice is 1/9.
- The probability of rolling a sum of 11 on two fair six-sided dice is 1/18.
- The probability of rolling a sum of 6 or more on two fair six-sided dice is 5/6.
- The probability of rolling a sum of 8 or more on two fair six-sided dice is 5/6.
- The probability of rolling a sum of 9 or less on two fair six-sided dice is 25/36.
- The probability of rolling a sum of 10 or more on two fair six-sided dice is 11/36.
- The probability of rolling a sum of 11 or less on two fair six-sided dice is 31/36.
- The probability of rolling a sum of 4 or less on two fair six-sided dice is 11/36
- The probability of rolling a sum of 5 or more on two fair six-sided dice is 31/36.
- The probability of rolling a sum of 7 on two fair six-sided dice is 1/6.
- The probability of rolling a sum of 3 on two fair six-sided dice is 2/36.
- The probability of rolling a sum of 8 on two fair six-sided dice is 5/36.
- The probability of rolling a sum of 12 on two fair six-sided dice is 1/36.
- The probability of rolling a sum of 5 on two fair six-sided dice is 4/36.
- The probability of rolling a sum of 10 on two fair six-sided dice is 1/12.
- The probability of rolling a sum of 4 on two fair six-sided dice is 3/36.
- The probability of rolling a sum of 9 on two fair six-sided dice is 4/36.
- The probability of rolling a sum of 6 on two fair six-sided dice is 5/36.
- The probability of rolling a sum of 11 on two fair six-sided dice is 2/36.
- The probability of rolling a sum of 2 on two fair six-sided dice is 1/36.
- The probability of rolling a sum of 7 or 11 on two fair six-sided dice is 1/9.
- The probability of rolling a sum of 6 or 8 on two fair six-sided dice is 1/4.
- The probability of rolling a sum of 7, 11, or 12 on two fair six-sided dice is 1/4.
- The probability of rolling a sum of 9 or 10 on two fair six-sided dice is 1/4.
- The probability of rolling a sum of 5 or 9 on two fair six-sided dice is 2/9.
- The probability of rolling a sum of 8 or 12 on two fair six-sided dice is 1/9.
- The probability of rolling a sum of 3 or 10 on two fair six-sided dice is 1/9.
- The probability of rolling a sum of 4 or 7 on two fair six-sided dice is 1/3.

### Interpretation

In the world of dice rolls, probabilities dance like capricious sprites around the numbers etched on each side. With a roll of two fair six-sided dice, the whims of fate reveal themselves in fractions and ratios, granting insight into the elusive nature of chance. From the elusive allure of a sum of 12, only a magical 1/36 chance, to the humble probability of landing on a 7 at a modest 1/6, these statistics paint a whimsical tapestry of mathematical intrigue. So next time you feel the urge to roll the dice, remember, behind each throw lies a world of probabilities waiting to unfold their enigmatic secrets.

## Probability of specific outcomes on fair six-sided dice

- The probability of rolling a 2 on a fair six-sided dice is 1/6.
- The probability of rolling a 6 when throwing a fair six-sided dice is 1/6.
- The probability of rolling an odd number on a fair six-sided dice is 1/2.
- The probability of rolling a prime number on a fair six-sided dice is 1/2.
- The probability of rolling a 5 or 6 on a fair six-sided dice is 1/3.
- The probability of rolling a 3 or 4 on a fair six-sided dice is 1/3.
- The probability of rolling a 2, 3, or 4 on a fair six-sided dice is 1/2.
- The probability of rolling a 1 or 6 on a fair six-sided dice is 1/3.
- The probability of rolling a 5 on a fair six-sided dice is 1/6.
- The probability of rolling a 2 or 5 on a fair six-sided dice is 1/3.
- The probability of rolling a 2 or 4 on a fair six-sided dice is 1/3.
- The probability of rolling a 1, 2, or 3 on a fair six-sided dice is 1/2.
- The probability of rolling a 3 on a fair six-sided dice is 1/6.
- The probability of rolling a 4 on a fair six-sided dice is 1/6.
- The probability of rolling a 5 on a fair six-sided dice is 1/6.
- The probability of rolling a 6 on a fair six-sided dice is 1/6.
- The probability of rolling a number less than 3 on a fair six-sided dice is 1/3.
- The probability of rolling an even number on a fair six-sided dice is 1/2.
- The probability of rolling a number greater than 4 on a fair six-sided dice is 1/3.
- The probability of rolling a multiple of 3 on a fair six-sided dice is 1/3.
- The probability of rolling a prime number on a fair six-sided dice is 1/2.
- The probability of rolling a number less than 4 on a fair six-sided dice is 1/2.
- The probability of rolling an odd number on two fair six-sided dice is 1/2.

### Interpretation

In the whimsical world of dice rolls, probabilities dance like fickle sprites, teasing us with their elusive patterns. From the stately allure of prime numbers to the mischievous charm of odd or even outcomes, each roll tells a tale of chance and mystery. The dice, those fickle diviners of fate, offer us a glimpse into the swirling maelstrom of possibilities, where the allure of a 6 or the simplicity of a 1 beckons like an enigmatic riddle waiting to be solved. So, let us roll the dice of destiny and see what secrets they hold, for in the realm of probability, even the most seemingly random outcomes may whisper a deeper truth we have yet to uncover.

## Probability of specific sums on two fair six-sided dice

- The probability of rolling a sum of 12 or more on two fair six-sided dice is 1/6.
- The probability of rolling a sum of 3 or 4 on two fair six-sided dice is 1/12.

### Interpretation

In the unpredictable world of dice rolls, the probability of hitting the jackpot with a sum of 12 or more is akin to spotting a unicorn in a crowded city street – rare and utterly delightful. On the flip side, the chances of landing a petite sum of 3 or 4 are as common as finding loose change in your couch cushions – not terribly exciting, but it's something. So, next time you roll the dice, remember that statistics can both surprise and comfort you, much like finding unexpected joy in mundane moments.