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# What is the probability of a regular 6-sided dice rolled three 6s in arow?

Updated: 12/7/2022

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Elizabeth Roberts

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2y ago

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13y ago

(1/6)*(1/6)*(1/6)=1/216

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Q: What is the probability of a regular 6-sided dice rolled three 6s in arow?
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### A die is rolled three times what is the probability of rolling three ones?

(1/6)^3 since each event is independent and each has a probability of 1/6.

50% chance

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The probability of rolling a six is one in six. The probability of rolling three consecutive sixes is one in 216. (1/6 x 1/6 x 1/6 = 1/216)

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The probability is 1 and you do not need Matlab to get that answer - only a little bit of thought.

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The first roll doesn't matter for probability, it just sets the number to be rolled by the other two. So: P(rolling the same number three times) = P(rolling a particular number)2 = (1/6)2 = 1/36

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There are two possibilities for rolling three once, so the probability of this even is 2/36 or 1/18. Since each roll is an independent event, the total probability is: P(rolling three three times) = (1/18)3 = 1/5832

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The answer depends on how many times in total the dice are rolled. As the total number of rolls increases, the probability rolling a 6 and 4 three times in a row increases towards 1.

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### Probability of two tetrahedral dice rolled the sum on the upward faces is four?

When a tetrahedral die is rolled, it will rest with three faces upwards. If the die is numberd from 1 to 4. therefore the sum of the upward facing numbers on 1 die is at least 6 and so for two dice, the minimum is 12. That being the case, the probability is 0.

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If using regular dice, the probability is 0 since the minimum sum from four dice is 4.

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It is (1/6)5 = 1/7776 = 0.00013 approx.