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Q: If a dice is rolled three times what is the probability of rolling a 3 each time?

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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)

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

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.

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

the chances of rolling doubles once is 1 in 6; 3 times in a row it is 1 in 216. It does not make any difference after how many times you rolled the dice before.

25/36

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

It is 0.8217

The probability of rolling a 6 is 1/6. The probability of rolling 10 times a 6 is (1/6)10 or 1.654X10-8.

15

The probability of rolling a 5, based on the information given, is 80/375 or 16/75. Your problem describes a relative frequency approximation of probability.

The probability of rolling a six is 1 out of 6, or 1/6. Now, perhaps your question is: If I roll a die 180 times, what is the probability of rolling a six at least once. This is the same as rolling a die 180 times and never once rolling a six. The probability is (5/6)180 which is 5.59 x 10-15.

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