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What is the hardest number to roll on a dice?

Dice Roll Probability Likewise, there is only one combination that yields a total of 12—when each die displays a 6. They are the least likely combinations to occur. As you can see, 7 is the most common roll with two six-sided dice.

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Rolling two six-sided dice is common in many of the most popular board games, including Monopoly, Backgammon and The Settlers of Catan. Even if you don't memorize the percentages in the chart below, it's helpful to have a general sense of how common each roll is. When it is your turn and you are two spaces away from landing on an opponent's hotel in Monopoly, this probability chart may comfort you.

Dice Roll Probability

The chance of rolling a total of 2 is 2.78 percent

The chance of rolling a total of 3 is 5.56 percent

The chance of rolling a total of 4 is 8.33 percent

The chance of rolling a total of 5 is 11.11 percent

The chance of rolling a total of 6 is 13.89 percent

The chance of rolling a total of 7 is 16.67 percent

The chance of rolling a total of 8 is 13.89 percent

The chance of rolling a total of 9 is 11.11 percent

The chance of rolling a total of 10 is 8.33 percent

The chance of rolling a total of 11 is 5.56 percent

The chance of rolling a total of 12 is 2.78 percent

There's only one combination that yields a total of 2—when each die displays a 1. Likewise, there is only one combination that yields a total of 12—when each die displays a 6. They are the least likely combinations to occur. As you can see, 7 is the most common roll with two six-sided dice. You are six times more likely to roll a 7 than a 2 or a 12, which is a huge difference. You are twice as likely to roll a 7 as you are to roll a 4 or a 10. However, it's only 1.2 times more likely that you'll roll a 7 than a 6 or an 8. Another way of looking at these numbers is that, over time, you will roll one 4 or 10 for every two 7s rolled. You'll see six 7s for every 2 or 12. Of course, dice have a bad habit of defying expectations, so don't rely on probabilities from a chart like this to work out your game strategy. You're likely to find yourself on the losing end of a game if you do.

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Does anything have a 0 percent chance of happening?

An event with a probability of zero [P(E) = 0] will never occur (an impossible event). An event with a probability of one [P(E) = 1] means the event must occur (a certain event). An event with a probability of 0.5 [P(E) = 0.5] is sometimes called a fifty-fifty chance event or an even chance event.

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Probability (of an event)

Definition

If P(E) represents the probability of an event E, then 0 ≤ P(E) ≤ 1. The probability of an event is the likelihood of that event occuring. Probability is a value between (and including) zero and one.

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An experimental probability is measured.

A theoretical probability is calculated.

An event with a probability of zero [P(E) = 0] will never occur (an impossible event). An event with a probability of one [P(E) = 1] means the event must occur (a certain event). An event with a probability of 0.5 [P(E) = 0.5] is sometimes called a fifty-fifty chance event or an even chance event. An event with a higher probability is more likely to occur than one with a lower probability.

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