The probability of rolling three sixes in a row on six-sided dice is 1/216 or approximately 0.0046. This is because there is only one combination out of 216 possible outcomes that results in three sixes.

The probability of rolling three sixes in a row on a six-sided dice can be calculated by finding the probability of getting a six on each individual roll and multiplying them together. Since each roll of the dice is an independent event, the probability of getting a six on a single roll is 1/6. Therefore, the probability of rolling three sixes in a row can be calculated as (1/6) * (1/6) * (1/6) = 1/216, or approximately 0.0046.

To further explore the topic of rolling dice and probabilities, let’s delve into some interesting facts and a quote from a well-known resource:

- Dice have been used for thousands of years, with the oldest known dice dating back to around 3000 BC in Egypt.
- The typical six-sided dice we use today are also known as “d6” dice, with each face showing a different number of dots, ranging from one to six.
- Probability is a branch of mathematics that deals with the likelihood of events occurring. It helps in analyzing and predicting outcomes in various fields, including gambling, statistics, and decision-making.
- The concept of probability was formalized by mathematician Blaise Pascal and mathematician Pierre de Fermat in the 17th century, opening a new field of study.
- Probability can be expressed as a fraction, a decimal, or a percentage. It ranges from 0 (impossible event) to 1 (certain event).
- Probability can be further classified as theoretical probability (based on calculations and assumptions) and experimental probability (based on actual observations).
- In gaming and gambling, understanding probability can help individuals make more informed decisions, whether it be placing bets, strategizing, or assessing risks.

Quote:

“The idea that the future is unpredictable is undermined every day by the ease with which the past is explained.” – Daniel Kahneman

Table:

Dice Rolls | Probability |
---|---|

One roll | 1/6 (0.1667) |

Two rolls | (1/6) * (1/6) = 1/36 (0.0278) |

Three rolls | (1/6) * (1/6) * (1/6) = 1/216 (0.0046) |

Remember, probabilities indicate the likelihood of an event occurring and can be a useful tool in decision-making and analyzing outcomes.

## Response to your question in video format

This video discusses the problem of rolling a die nine times and finding the probability of getting exactly two sixes. Unlike the previous coin flipping problem, the probability of getting a six is 1/6 while the probability of not getting a six is 5/6. There are multiple combinations of getting two sixes out of nine rolls, which is determined using the combination formula. To find the probability, the number of combinations is multiplied by the probability of the event occurring. The result is approximately 0.2792, demonstrating how to deal with unequal probabilities in such cases.

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1/216Probability of getting 6 three times in a row = (1/6) × (1/6) × (1/6) = 1/216.

## I am sure you will be interested in this

*133*. It’s (1/3)³ .

*0.01286%*.

Probability of getting 1 three times in a row = probability of getting 1 first time × probability of getting 1 second time × probability of getting 1 third time. Probability of getting 1 three times in a row = (1/6) × (1/6) × (1/6) = 1/216. Hence, the probability of getting 1 three times in a row is 0.463%.

*1/216*so they would be our odds.

*1/8*after reducing the fraction, as mentioned in the video.

*all the same!*But if the number of odd and even sides are not equal (if the dice has an odd number of sides) then there is not the same probability! The more sides, the closer the fraction will get to 1/2, but it will never be 1/2!

*0.463%*. Question 1: What is the probability of rolling a 5 on a dice 3 times? Probability of an event = (number of favourable event) / (total number of event). P (B) = (Event B) / (total number of event).

*36*different rolls with two dice, with any sum from 2 to 12 possible. How does the problem change if we add more dice? Just as one die has six outcomes and two dice have 6 2 = 36 outcomes, the probability experiment of rolling three dice has 6 3 = 216 outcomes.